bonjour,
f (x) = 2 x² + 4 x - 6
g (x) = 2 ( x + 1 )² - 8 = 2 ( x² + 2 x + 1 ) - 8
= 2 x² + 4 x + 2 - 8 = 2 x² + 4 x - 6
h (x )= 2 ( x - 1 ) ( x + 3) = ( 2 x - 2 ) ( x + 3 ) = 2 x² + 6 x - 2 x - 6 = 2 x² + 4 x - 6
a) ( 2 x - 2 ) ( x + 3 ) = 0 lorsque x vaut 1 ou - 3
2 x² + 4 x - 6 = - 6
2 x² + 4 x - 6 + 6 = 0
2 x ( x + 4 ) = 0 quand x = 0 ou - 4
b) f(0) = - 6
f ( 1 ) = 2 + 4 - 6 = 0
f ( √3 - 1 ) = 2 ( √3 - 1 )² + 4 (√3 - 1 ) - 6
= 2 ( 3 - 2 √3 + 1 ) + 4√3 - 4 - 6
= 6 - 4 √3 + 2 + 4√3 - 10 = - 2
c) 2 x² + 4 x - 6 = 24
2 x² + 4 x = 30
2 x² + 4 x - 30 = 0
Δ = 16 - 4 ( 2 * - 30 ) = 16 + 240 = 256
x 1 = ( - 4 - 16) / 4 = - 20/4 = - 5
x 2 = ( - 4 + 16 ) / 4 = 12 /4 = 3
abscisses = - 5 et 3
