Question
B(x)=-2x²+4x+8x-16+x-2
1)Factoriser B(x)
2)Résoudre l'équation B(x)=0
1)Factoriser B(x)
2)Résoudre l'équation B(x)=0
Asked by: USER4747
87 Viewed
87 Answers
Answer (87)
Bonjour Karl58
[tex]1)\ B(x)=-2x^2+4x+8x-16+x-2\\\\B(x)=-2x^2+4x+8x+x-16-2\\\\B(x)=-2x^2+13x-18\\\\B(x)=-2x^2+(9x+4x)-18\\\\B(x)=(-2x^2+9x)+(4x-18)\\\\B(x)=-x(2x-9)+2(2x-9)\\\\\boxed{B(x)=(2x-9)(-x+2)}[/tex]
[tex]2)\ B(x)=0\\\\(2x-9)(-x+2)=0\\\\2x-9=0\ \ ou\ \ -x+2=0\\\\2x=9\ \ ou\ \ -x=-2\\\\\boxed{x=\dfrac{9}{2}\ \ ou\ \ x=2}\\\\\boxed{x=4,5\ \ ou\ \ x=2}[/tex]
[tex]1)\ B(x)=-2x^2+4x+8x-16+x-2\\\\B(x)=-2x^2+4x+8x+x-16-2\\\\B(x)=-2x^2+13x-18\\\\B(x)=-2x^2+(9x+4x)-18\\\\B(x)=(-2x^2+9x)+(4x-18)\\\\B(x)=-x(2x-9)+2(2x-9)\\\\\boxed{B(x)=(2x-9)(-x+2)}[/tex]
[tex]2)\ B(x)=0\\\\(2x-9)(-x+2)=0\\\\2x-9=0\ \ ou\ \ -x+2=0\\\\2x=9\ \ ou\ \ -x=-2\\\\\boxed{x=\dfrac{9}{2}\ \ ou\ \ x=2}\\\\\boxed{x=4,5\ \ ou\ \ x=2}[/tex]
voila la réponse il suffi d'utiliser le discriminat delta et ytiliser la regle a(x-x1)(x-x2)
