bonjour
f (x) = ( x - 2) ( x + 6)
f (x) = x² + 6 x - 2 x - 12 = x² + 4 x - 12
f (x) = ( x + 2)² - 16 = ( x + 2 - 4 ) ( x + 2 + 4 ) = ( x - 2 ) ( x + 6 )
f (x) ≤ 0
x - 2 = 0 pour x = 2 et x + 6 = 0 pour x = - 6
S [ - 6 , 2 ]
f (x) ≤ 20
x² - 4 x - 12 ≤20
x² - 4 x - 12 - 20 ≤0
x² - 4 x - 32 ≤ 0
Δ : 16 - 4 ( 1 * -32) = 16 + 128 = 144 = 12 ²
x 1 = ( 4 + 12)/2 = 16/2 = 8
x 2 = ( 4 - 12)/2 = - 8/2 = - 4
S ( - 4 ; 8)
f (x) ≤ x² + 4
x² + 4 x - 12 ≤ x² + 4
x² - x² + 4 x ≤ 4 + 12
4 x ≤ 16
x ≤ 4
S ] - ∞ ; 4 ]
