bonsoir
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 ( x² + 3 x - x - 3 ) = 2 x² + 6 x - 2 x - 6 = 2 x² + 4 x - 6
a) 2 ( x - 1 ) ( x + 3 ) = 0 ⇔ x = 1 ou - 3
2 x² + 4 x - 6 = - 6
2 x² + 4 x = 0
2 x ( x + 2 ) = 0 ⇔ x = 0 ou - 2
b ) f (0) = - 6
f ( 1 ) = 2 *1² + 4 *1 - 6 = 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 - 6 - 24 = 0
2 x² + 4 x - 30 = 0
Δ = 16 - 4 ( 2 * - 30 ) = 16 + 240 =256 = 16²
x 1 = ( - 4 - 16 ) / 4 = - 20 /4 = - 5
x 2 = ( - 4 + 16 ) /4 = 12 /4 = 3
S ( - 5 : 3 )
