Pierwiastkami wielomianu W(x) = x³ +px + q są liczby x1, x2, x3 spełniające warunki x2 = x1, x3 = x1 - 6 Oblicz log½(p+q) + wszystkie obliczenia;)

załącznik.

W(x) = x³+px+q W(x) = (x-x₁)(x-x₂)(x-x₃) x₁=x₂ x₃=x₁-6 W(x) = (x-x₁)²(x-x₁+6) = (x²-2x₁x+x₁²)(x-x₁+6) = = x³-x₁x²+6x²-2x₁x²+2x₁²x-12x₁x+x₁²x-x₁³+6x₁² = = x³+(-x₁+6-2x₁)x²+(2x₁²-12x₁+x₁²)x-x₁³+6x₁² = = x³+(6-3x₁)x²+(3x₁²-12x₁)x-x₁³+6x₁² 6-3x₁ = 0 <=> x₁ = 2 3x₁²-12x₁ = p <=> p = -12 -x₁³+6x₁² = q <=> q = 16 log½(p+q) = log½(4) = log½((½)⁻²) = -2