Wie berechne ich die Schnittstellen von 2 Funktionen

Question

wie berechne ich die Schnittstellen von

f(x)=x^3-5*x^2+6*x  und  g(x)=1,75*x+1

ich weiß, dass ich gleichsetzen muss, komme dann aber nicht weiter!

Answer 1

x^3 - 5·x^2 + 6·x = 1.75·x + 1
x^3 - 5·x^2 + 4.25·x - 1 = 0

Eine Nullstelle findest du per Wertetabelle bei 4 und machst eine Polynomdivision

(x^3 - 5·x^2 + 4.25·x - 1)/(x - 4) = x^2 - x + 0.25

Die restliche(n) Nullstelle(n) liefert jetzt die pq-Formel bei x = 0.5.

Comments

Super!

Answer 2

Hallo,

gleichsetzen, dann alles auf Null, Polynomdivision durchführen

x³-5x²+6x= 1,75x +1  

x³-5x² +4,25 x -1   = 0    

1/4 (4x³ -20x² +17x -4)

Polynomdivision durchführen mit (x - 4)    , dann pq-Formel anwenden

Lösungen L= { 0,5 , 4} 

     

Answer 3

gleichgesetzt f(x)=g(x)

x³-5*x²+6*x=1,75*x+1

0=x³-5*x²+6*x-1,75*x-1

0=x³-5*x²+4,25*x-1 Lösung mit meinem Graphikrechner (GTR,Casio) x1=0,5 und x2=4

Oft sind die Nullstellen keine ganzen Zahlen und dann muß man eine Nullstelle angenähert durch probieren ermitteln und dann den Wert durch einer der beiden Näherungsformeln von

Newton (Tangentenverfahren) oder Regula falsi (Sehenverfahren)

Hier Infos per Bild,vergrößern und/oder herunterladen

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