Odpowiedź:
Podpunkt 4.1
P(x) = a₃x³ +a₂x² + a₁x + a₀
a₃ = 5
a₂ = 1
a₁ = - 10
a₀ = - 2
P(x) = 5x³ + x² + (- 10x - 2) = 5x³ + x² - 2(5x + 1) = x²(5x + 1) - 2(5x + 1) =
= (5x + 1)(x² - 2) = (5x + 1)(x - √2)(x +√2)
(5x + 1)(x - √2)(x + √2) = 0
5x + 1 = 0 ∨ x - √2 = 0 ∨ x + √2 = 0
x = - 1/5 ∨ x = √2 ∨ x = - √2
x = - √2 najmniejszy pierwiastek
Podpunkt 4.2
x = √2 najwiekszy pierwiastek
