Odpowiedź:
Szczegółowe wyjaśnienie:
Zad 6
x² - 5x + 36 = 0
Δ = 25 - 144 < 0 ⇒ x ∈ ∅
Zad 7
x² + 3x - 10 = 0
Δ = 9 + 40 = 49 ⇒ √Δ = 7
x₁ = (-3-7)/2 = -5
x₂ = (-3+7)/2 = 2
x₁x₂ = c/a = -10/1 = -10
x₁x₂ = -5*2 = -10
Zgadza się.
x₁ + x₂ = -b/a = -3/1 = -3
x₁ + x₂ = -5 + 2 = -3
Zgadza się.
Zad 8
4x⁴ - 13x² + 3 = 0, t = x², t ≥ 0
4t² - 13t + 3 = 0
Δ = 169 - 48 = 121 ⇒ √Δ = 11
t₁ = (13-11)/8 = 1/4
t₂ = (13+11)/8 = 3
x² = 1/4 ∨ x² = 3
x = -1/2 ∨ x = 1/2 ∨ x = -√3 ∨ x = √3
