bonjour
A(x) = 2 ( x + 3 )² + 6 + 2 x
1 ) A (x) = 2 ( x + 3 ) ( x + 3 ) + 2 ( 3 + x )
A ( x) = ( x + 3 ) ( 2 x + 6 + 2 )
A ( x ) = ( x + 3 ) ( 2 x + 8 )
2/ A (x) = 2 ( x² + 6 x + 9) + 6 + 2 x
A (x) = 2 x² + 12 x + 18 + 6 + 2 x
a (x) = 2 x² + 14 x + 24
A (1) = 2*1² + 14 *1 + 24 = 2 + 14 + 24 = 40
A ( √7) = 2 ( √7)² + 14√7 + 24
A ( √7) = 14 + 14√7 + 24 = 38 + 14 √7
A(x) = 0
( x + 3 ) ( 2 x + 8) = 0
soit x + 3 = 0 et x = - 3
soit 2 x + 8 = 0 ⇔ 2 x = - 8 ⇔ x = - 8/2 = - 4
S ( - 3 ; - 4)
A(x) > 24
2 x² + 14 x + 24 > 24
2 x² + 14 x + 24 - 24 > 0
2 x² + 14 x > 0
2 x ( x + 7 ) >0
2 x = 0 quand x = 0
x + 7 = 0 quand x = - 7
S ] - ∞ ; - 7 [ ∪ ] 0 ; + ∞ [
