bonjour
j'en fais un
A (x) = ( 2 x - 5 ) ( 2 x + 5 ) - ( 2 x - 5 ) ( x + 4 )
1 . A (x) = 4 x² - 25 - ( 2 x² + 8 x - 5 x - 20 )
A ( x ) = 4 x² - 25 - 2 x² - 8 x + 5 x + 20
A (x) = 2 x² - 3 x - 5
2. A (x) = ( 2 x - 5 ) ( 2 x + 5 - x - 4 )
A (x) = ( 2 x - 5 ) ( x + 1 )
x = 0 ⇔ A = - 5 * 1 = - 5
x = - 1 ⇔ A = - 7 * 0 = 0
x = 1/4 ⇔ A = 2 * ( 1/4)² - 3 * 1/4 - 5 = 2 * 1/16 - 3 /4 - 5 = 1/8 - 6/8 - 40/8
= - 45 /8
x = - √5 ⇔ A = 2 ( - √5 )² - 3 ( - √5) - 5 = 10 + 3 √5 - 5 = 5 + 3 √5
A (x) = 0
( 2 x - 5 ) ( x + 1 ) = 0 ⇔ x = 5/2 ou - 1
A (x) = - 5
2 x² - 3 x - 5 = - 5
⇔ x ( 2 x - 3 ) = 0 ⇔ x = 0 ou 3/2
