Bonsoir,
On considère la fonction f(x)=(2x-3)(5-x)-x(5-x)
1:développer f(x)
f(x) = 10x - 2x^2 - 15 + 3x - 5x + x^2
f(x) = -x^2 + 8x - 15
2: factoriser f(x)
f(x) = (5 - x)(2x - 3 - x)
f(x) = (5 - x)(x - 3)
Résoudre les équations:
F(x)=-15
-x^2 + 8x - 15 = -15
-x^2 + 8x = 15 - 15 = 0
x(-x + 8) = 0
x = 0 ou -x + 8 = 0
x = 0 ou x = 8
F(x)=0
(5 - x)(x - 3) = 0
5 - x = 0 ou x - 3 = 0
x = 5 ou x = 3
