Bonjour,
1) f(x) = 2x² + 4x - 5
= 2(x² + 2x - 5/2)
= 2[(x + 1)² - 1 - 5/2]
= 2[(x + 1)² - 7/2]
2) f(x) = 2x² + 4x - 5
Δ = 4² - 4x2x(-5) = 16 + 40 = 56
2 solutions :
x₁ = (-4 - √56)/4 = -1 - √(14)/2 ≈ -2,87
et
x₂ = (-4 + √56)/4 = -1 + √(14)/2 ≈ 0,87
3) f(x) = 2(x - x₁)(x - x₂)
= 2(x + 1 + √(14)/2)(x + 1 - √14/2)
4)
x -∞ x₁ x₂ +∞
x - x₁ - 0 + +
x - x₂ - - 0 +
f(x) + 0 - 0 +
5) ci-joint
Sommet : S(-1 ; -7)
