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<link type="text/css" rel="stylesheet" href="http://pasterack.org/scribble.css"/><link type="text/css" rel="stylesheet" href="http://pasterack.org/racket.css"/><link type="text/css" rel="stylesheet" href="http://fonts.googleapis.com/css?family=Droid+Sans+Mono"/><div style="font-family:'Droid Sans Mono',monospace;background-color:transparent"><ol start="0" style="font-size:70%;color:#A0A0A0"><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><a class="RktModLink" data-pltdoc="x" href="http://docs.racket-lang.org/guide/Module_Syntax.html#%28part._hash-lang%29"><span class="RktMod">#lang</span></a><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><a class="RktModLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/index.html"><span class="RktSym">racket</span></a><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"> </span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="RktCmt">;;</span><span class="hspace"> </span><span class="RktCmt">[hier</span><span class="hspace"> </span><span class="RktCmt">ergaenzen</span><span class="hspace"> </span><span class="RktCmt">und</span><span class="hspace"> </span><span class="RktCmt">weitere</span><span class="hspace"> </span><span class="RktCmt">Beispiele</span><span class="hspace"> </span><span class="RktCmt">erzeugen]</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="RktCmt">;;</span><span class="hspace"> </span><span class="RktCmt">(pqformel</span><span class="hspace"> </span><span class="RktCmt">0</span><span class="hspace"> </span><span class="RktCmt">0</span><span class="hspace"> </span><span class="RktCmt">5)</span><span class="hspace"> </span><span class="RktCmt">sollte</span><span class="hspace"> </span><span class="RktCmt">einen</span><span class="hspace"> </span><span class="RktCmt">Fehler</span><span class="hspace"> </span><span class="RktCmt">"pqformel:</span><span class="hspace"> </span><span class="RktCmt">"keine</span><span class="hspace"> </span><span class="RktCmt">Loesung</span><span class="hspace"> </span><span class="RktCmt">-</span><span class="hspace"> </span><span class="RktCmt">gebe</span><span class="hspace"> </span><span class="RktCmt">eine</span><span class="hspace"> </span><span class="RktCmt">richtige</span><span class="hspace"> </span><span class="RktCmt">Gleichung</span><span class="hspace"> </span><span class="RktCmt">ein"</span><span class="hspace"> </span><span class="RktCmt">ergeben</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="RktCmt">;;</span><span class="hspace"> </span><span class="RktCmt">(pqformel</span><span class="hspace"> </span><span class="RktCmt">...</span><span class="hspace"> </span><span class="RktCmt">...</span><span class="hspace"> </span><span class="RktCmt">...)</span><span class="hspace"> </span><span class="RktCmt">sollte</span><span class="hspace"> </span><span class="RktCmt">einen</span><span class="hspace"> </span><span class="RktCmt">Fehler</span><span class="hspace"> </span><span class="RktCmt">"pqformel:</span><span class="hspace"> </span><span class="RktCmt">jedes</span><span class="hspace"> </span><span class="RktCmt">X"</span><span class="hspace"> </span><span class="RktCmt">ergeben</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="RktCmt">;;</span><span class="hspace"> </span><span class="RktCmt">(pqformel</span><span class="hspace"> </span><span class="RktCmt">...</span><span class="hspace"> </span><span class="RktCmt">...</span><span class="hspace"> </span><span class="RktCmt">...)</span><span class="hspace"> </span><span class="RktCmt">sollte</span><span class="hspace"> </span><span class="RktCmt">einen</span><span class="hspace"> </span><span class="RktCmt">Fehler</span><span class="hspace"> </span><span class="RktCmt">"pqformel:</span><span class="hspace"> </span><span class="RktCmt">keine</span><span class="hspace"> </span><span class="RktCmt">reelle</span><span class="hspace"> </span><span class="RktCmt">Loesung"</span><span class="hspace"> </span><span class="RktCmt">ergeben</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="RktCmt">;;</span><span class="hspace"> </span><span class="RktCmt">(pqformel</span><span class="hspace"> </span><span class="RktCmt">...</span><span class="hspace"> </span><span class="RktCmt">...</span><span class="hspace"> </span><span class="RktCmt">...)</span><span class="hspace"> </span><span class="RktCmt">sollte</span><span class="hspace"> </span><span class="RktCmt">...</span><span class="hspace"> </span><span class="RktCmt">ergeben</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"> </span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"> </span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="RktCmt">;;</span><span class="hspace"> </span><span class="RktCmt">Definition</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktStxLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/define.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._define%29%29">define</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym">pqformel</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">a</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">b</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">c</span><span class="RktPn">)</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="RktCmt">;;</span><span class="hspace"> </span><span class="RktCmt">(D</span><span class="hspace"> </span><span class="RktCmt">a</span><span class="hspace"> </span><span class="RktCmt">b</span><span class="hspace"> </span><span class="RktCmt">c)</span><span class="hspace"> </span><span class="RktCmt">wird</span><span class="hspace"> </span><span class="RktCmt">zur</span><span class="hspace"> </span><span class="RktCmt">Berechnung</span><span class="hspace"> </span><span class="RktCmt">der</span><span class="hspace"> </span><span class="RktCmt">Diskriminante</span><span class="hspace"> </span><span class="RktCmt">verwendet</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="RktCmt">;;</span><span class="hspace"> </span><span class="RktCmt">quadratische</span><span class="hspace"> </span><span class="RktCmt">und</span><span class="hspace"> </span><span class="RktCmt">lineare</span><span class="hspace"> </span><span class="RktCmt">Gleichungen</span><span class="hspace"> </span><span class="RktCmt">werden</span><span class="hspace"> </span><span class="RktCmt">unterschiedlich</span><span class="hspace"> </span><span class="RktCmt">geloest</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktStxLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/if.html#%28form._%28%28lib._racket%2Fprivate%2Fletstx-scheme..rkt%29._cond%29%29">cond</a></span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">[</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._~3d%29%29">=</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">a</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">0</span><span class="RktPn">)</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktCmt">;;</span><span class="hspace"> </span><span class="RktCmt">Ausnahme:</span><span class="hspace"> </span><span class="RktCmt">lineare</span><span class="hspace"> </span><span class="RktCmt">Gleichung,</span><span class="hspace"> </span><span class="RktCmt">die</span><span class="hspace"> </span><span class="RktCmt">mit</span><span class="hspace"> </span><span class="RktCmt">3</span><span class="hspace"> </span><span class="RktCmt">Moeglichkeiten</span><span class="hspace"> </span><span class="RktCmt">endet</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktStxLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/if.html#%28form._%28%28lib._racket%2Fprivate%2Fletstx-scheme..rkt%29._cond%29%29">cond</a></span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">[</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktStxLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/if.html#%28form._%28%28lib._racket%2Fprivate%2Fletstx-scheme..rkt%29._and%29%29">and</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._~3d%29%29">=</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">b</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">0</span><span class="RktPn">)</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._~3d%29%29">=</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">c</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">0</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/exns.html#%28def._%28%28quote._~23~25kernel%29._error%29%29">error</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym"><a class="RktStxLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/quote.html#%28form._%28%28quote._~23~25kernel%29._quote%29%29">'</a></span><span class="RktSym">pqformel</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">"jedes</span><span class="hspace"> </span><span class="RktVal">X"</span><span class="RktPn">)</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">]</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">[</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._~3d%29%29">=</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">b</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">0</span><span class="RktPn">)</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/exns.html#%28def._%28%28quote._~23~25kernel%29._error%29%29">error</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym"><a class="RktStxLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/quote.html#%28form._%28%28quote._~23~25kernel%29._quote%29%29">'</a></span><span class="RktSym">pqformel</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">"keine</span><span class="hspace"> </span><span class="RktVal">Loesung</span><span class="hspace"> </span><span class="RktVal">-</span><span class="hspace"> </span><span class="RktVal">gebe</span><span class="hspace"> </span><span class="RktVal">eine</span><span class="hspace"> </span><span class="RktVal">richtige</span><span class="hspace"> </span><span class="RktVal">Gleichung</span><span class="hspace"> </span><span class="RktVal">ein"</span><span class="RktPn">)</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">]</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktCmt">;;</span><span class="hspace"> </span><span class="RktCmt">falsche</span><span class="hspace"> </span><span class="RktCmt">Gleichung</span><span class="hspace"> </span><span class="RktCmt">]</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">[</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym"><a class="RktStxLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/if.html#%28form._%28%28lib._racket%2Fprivate%2Fletstx-scheme..rkt%29._else%29%29">else</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym">solve-linear-equation</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">b</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">c</span><span class="RktPn">)</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">]</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktCmt">;;</span><span class="hspace"> </span><span class="RktCmt">einfache</span><span class="hspace"> </span><span class="RktCmt">lineare</span><span class="hspace"> </span><span class="RktCmt">Loesung</span><span class="hspace"> </span><span class="RktCmt">-</span><span class="hspace"> </span><span class="RktCmt">einzige</span><span class="hspace"> </span><span class="RktCmt">Nullstelle</span><span class="hspace"> </span><span class="RktCmt">]</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">)</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">]</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktCmt">;;</span><span class="hspace"> </span><span class="RktCmt">a</span><span class="hspace"> </span><span class="RktCmt">ist</span><span class="hspace"> </span><span class="RktCmt">nicht</span><span class="hspace"> </span><span class="RktCmt">Null</span><span class="hspace"> </span><span class="RktCmt">-></span><span class="hspace"> </span><span class="RktCmt">loesen</span><span class="hspace"> </span><span class="RktCmt">eine</span><span class="hspace"> </span><span class="RktCmt">quadratische</span><span class="hspace"> </span><span class="RktCmt">Gleichung</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">[</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._~3e%29%29">></a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym">D</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">a</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">b</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">c</span><span class="RktPn">)</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">0</span><span class="RktPn">)</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym">find-roots</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">a</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">b</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym">D</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">a</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">b</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">c</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">]</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktCmt">;;</span><span class="hspace"> </span><span class="RktCmt">zwei</span><span class="hspace"> </span><span class="RktCmt">Nullstellen</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">[</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._~3c%29%29"><</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym">D</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">a</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">b</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">c</span><span class="RktPn">)</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">0</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">)</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/exns.html#%28def._%28%28quote._~23~25kernel%29._error%29%29">error</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym"><a class="RktStxLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/quote.html#%28form._%28%28quote._~23~25kernel%29._quote%29%29">'</a></span><span class="RktSym">pqformel</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">"keine</span><span class="hspace"> </span><span class="RktVal">reelle</span><span class="hspace"> </span><span class="RktVal">Loesung"</span><span class="RktPn">)</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">]</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">[</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym"><a class="RktStxLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/if.html#%28form._%28%28lib._racket%2Fprivate%2Fletstx-scheme..rkt%29._else%29%29">else</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym">find-1-root</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">a</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">b</span><span class="RktPn">)</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">]</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktCmt">;;</span><span class="hspace"> </span><span class="RktCmt">eine</span><span class="hspace"> </span><span class="RktCmt">einzige</span><span class="hspace"> </span><span class="RktCmt">Nullstelle,</span><span class="hspace"> </span><span class="RktCmt">d.h.</span><span class="hspace"> </span><span class="RktCmt">der</span><span class="hspace"> </span><span class="RktCmt">Scheitelpunkt</span><span class="hspace"> </span><span class="RktCmt">der</span><span class="hspace"> </span><span class="RktCmt">Parabel</span><span class="hspace"> </span><span class="RktCmt">liegt</span><span class="hspace"> </span><span class="RktCmt">and</span><span class="hspace"> </span><span class="RktCmt">der</span><span class="hspace"> </span><span class="RktCmt">x-Achse</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">)</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">)</span><span class="RktMeta"></span></span></li></ol><p>=></p><blockquote><table style="font-size:90%;table-layout:fixed;width:100%;word-wrap:break-word"></table></blockquote></div>
#lang
racket
;;
[hier
ergaenzen
und
weitere
Beispiele
erzeugen]
;;
(pqformel
0
0
5)
sollte
einen
Fehler
"pqformel:
"keine
Loesung
-
gebe
eine
richtige
Gleichung
ein"
ergeben
;;
(pqformel
...
...
...)
sollte
einen
Fehler
"pqformel:
jedes
X"
ergeben
;;
(pqformel
...
...
...)
sollte
einen
Fehler
"pqformel:
keine
reelle
Loesung"
ergeben
;;
(pqformel
...
...
...)
sollte
...
ergeben
;;
Definition
(
define
(
pqformel
a
b
c
)
;;
(D
a
b
c)
wird
zur
Berechnung
der
Diskriminante
verwendet
;;
quadratische
und
lineare
Gleichungen
werden
unterschiedlich
geloest
(
cond
[
(
=
a
0
)
;;
Ausnahme:
lineare
Gleichung,
die
mit
3
Moeglichkeiten
endet
(
cond
[
(
and
(
=
b
0
)
(
=
c
0
)
)
(
error
'
pqformel
"jedes
X"
)
]
[
(
=
b
0
)
(
error
'
pqformel
"keine
Loesung
-
gebe
eine
richtige
Gleichung
ein"
)
]
;;
falsche
Gleichung
]
[
else
(
solve-linear-equation
b
c
)
]
;;
einfache
lineare
Loesung
-
einzige
Nullstelle
]
)
]
;;
a
ist
nicht
Null
->
loesen
eine
quadratische
Gleichung
[
(
>
(
D
a
b
c
)
0
)
(
find-roots
a
b
(
D
a
b
c
)
)
]
;;
zwei
Nullstellen
[
(
<
(
D
a
b
c
)
0
)
(
error
'
pqformel
"keine
reelle
Loesung"
)
]
[
else
(
find-1-root
a
b
)
]
;;
eine
einzige
Nullstelle,
d.h.
der
Scheitelpunkt
der
Parabel
liegt
and
der
x-Achse
)
)
=>