Réponse :
D = ( 2-5x ) ( 4x + 3 ) - ( 2-5x )²
1/ D = ( 2-5x ) ( 4x + 3 ) - ( 2-5x )²
= 2*4x+3*2 -5x*4x-5x*3 - 2² -2*(2*5x) +(5x)²
=8x + 6 -20x²-15x-4-2*10x + 25x²
= -20x² + 8x -15x + 6 -4 -20x +25x²
=5x² -7x+2
2/ D = ( 2-5x ) ( 4x + 3 ) - ( 2-5x )²
= ( 2-5x ) ( ( 4x + 3 ) - ( 2-5x ) )
= ( 2-5x ) ( 4x +3 -2+5x )
= ( 2-5x ) ( 9x +1 )
3/ ( 2-5x ) ( 9x + 1 ) = 0
2-5x = 0 ou 9x + 1 = 0
-5x = -2 9x = -1
x = -2/-5 x = -1/9
x = 2/5
4/ avec x = -1
5x² -7x+2 = 5*(-1)² - 7*(-1) + 2 = 5 + 7 + 2 = 14
avec x = 1/3
5x² -7x+2 = 5* ( 1/3)² - 7*1/3 + 2 = 1/9 -7/3 + 2 = 1/9 - 21/9 + 2/1 = -20/9 + 18/9 = -2/9
