Răspuns:
x ∈ [-4 ; -3] ∪ [1 ; 2]
Explicație pas cu pas:
(x² - 3x + 2)(x² + 7x + 12) ≤ 0
1) x² - 3x + 2 = 0
a = 1 ; b = -3 ; c = 2
Δ = b²-4ac = (-3)²-4·1·2 = 9-8 = 1
√Δ = 1
x₁,₂ = (-b±√Δ)/2a = (3±1)/2 =>
x₁ = (3-1)/2 = 2/2 = 1
x₂ = (3+1)/2 = 4/2 = 2
2) x² + 7x + 12 = 0
a = 1 ; b = 7 ; c = 12
Δ = 49-48 = 1 ; √Δ = 1
x₁,₂ = (-7±1)/2 => x₁ = -8/2 = -4 ; x₂ = -6/2 = -3
3)
x I -∞ -4 -3 1 2 +∞
x² - 3x + 2 I+++++++++++++++++++++0----0+++++++++++
x² + 7x + 12 I++++++++++++0------0+++++++++++++++++++
(x² - 3x + 2)(x² + 7x + 12) I++++++++++++ 0------0+++0-----0++++++++++
=> x ∈ [-4 ; -3] ∪ [1 ; 2]
