ПОВТОРЮЄМО АЛГЕБРУ ЗА 8 КЛАС: 67

67. Розкладіть на множники квадратний тричлен:

1) x² – 7x + 6 = (x – 1)(x – 6);

x₁ + x₂ = 7; x₁ • x₂ = 6;

x₁ = 1; x₂ = 6.

2) 2x² + 5x + 2 = 2(x + $\frac{1}{2}$)(x + 2) = (2x + 1)(x + 2).

D = 5² – 4 • 2 • 2 = 25 – 16 = 9.

x₁ = $\frac{-5-\sqrt{9}}{2•2}$ = $\frac{-5-3}{4}$ = $\frac{-8}{4}$ = –2;

x₂ = $\frac{-5+3}{4}$ = $\frac{-2}{4}$ = –$\frac{1}{2}$.

3) –3x² – 5x + 2 = –3(x – $\frac{1}{3}$)(x + 2) = (–3x + 1)(x + 2);

D = (–5)² – 4 • (–3) • 2 = 25 + 24 = 49;

x₁ = $\frac{5-\sqrt{49}}{2•(-3)}$ = $\frac{5-7}{-6}$ = $\frac{-2}{-6}$ = $\frac{1}{3}$;

x₂ = $\frac{5+7}{-6}$ = $\frac{12}{-6}$ = –2.