bonjour
f (x) = x² + 5 x - 6
f (x) = ( x - 1 ) ( x + 6 )
f (x ) = x² + 6 x - x - 6 = x² + 5 x - 6
f (x) = ( x + 5/2 )² - 49/4
f (x) = x² + 10 x /2 + 25/4 - 49 /4
f (x) = x² + 5 x - 24/4 = x² + 5 x - 6
f (- 6 ) = ( - 6 )² + 5 ( - 6 ) - 6 = 36 - 30 - 6 = 0
f ( 0) = - 6
f ( 5/2) = ( 5/2)² + 5 * 5/2 - 6 = 25/4 + 25/2 - 6
f ( 5/2 ) = 25/4 + 50/4 - 24/4 = 51/4
f (x) = 0
( x - 1 ) ( x + 6 ) = 0
x = 1 ou - 6
f (x) = - 6
x² + 5 x - 6 = - 6
x² + 5 x = 0
x ( x + 5 ) = 0
x = 0 ou - 5
f (x) = 15/4
( x + 5/2)² - 49/4 = 15/4
( x + 5/2 )² - 49/ 4 - 15 /4 = 0
( x + 5/2 )² - 64/ 4 = 0
( x + 5/2 )² - ( 8/2 )² = 0
( x + 5/2 + 8/2 ) ( x + 5/2 - 8/2 ) = 0
( x + 13 /2 ) ( x - 3 /2 ) = 0
x = - 13/2 ou 3 /2
