x² + 12x + 27 ≥ 0 ?
french reasoning
it is necessary to factorize therefore to seek the roots of the polynomial
Δ = 12² - 4*1*27 = 144 - 108 = 36 = 6²
x' = (-12 + 6)/2 = -3
x'' = (-12 - 6)/2 = -9
so x² + 12x + 27 = (x + 3) (x + 9)
x - inf -9 -3 + inf
x+3 - - 0 +
x+9 - 0 + +
( ) ( ) + 0 - 0 +
x² + 12x + 27 ≥ 0 on ] -inf ; - 9 ] U [- 3 ; + inf [
on a graph
XXXXXXXXXX - 9.............-3 XXXXXXXXX
