Повторюємо алгебру за 8 клас: 68

68. Розкладіть на множники квадратний тричлен:

1) x² – 5x – 6 = (x + 1)(x – 6);

x₁ + x₂ = 5; x₁ • x_{2 =} –6;

x₁ = –1; x₂ = 6.

2) 3x² – 4x + 1 = 3(x – $\frac{1}{3}$)(x – 1) = (3x – 1)(x – 1);

D = (–4)² – 4 • 3 • 1 = 16 – 12 = 4.

x₁ = $\frac{4-\sqrt{4}}{2•3}$ = $\frac{4-2}{6}$ = $\frac{2}{6}$ = $\frac{1}{3}$;

x₂ = $\frac{4+\sqrt{4}}{2•3}$ = $\frac{4+2}{6}$ = $\frac{6}{6}$ = 1.

3) –2x^{2 +} 7x – 3 = –2(x – $\frac{1}{2}$)(x – 3) = (–2x + 1)(x – 3) = (1 – 2x)(x – 3).

D = 7² – 4 • (–2) • (–3) = 49 – 24 = 25.

x₁ = $\frac{-7-\sqrt{25}}{2•(-2)}$ = $\frac{-7-5}{-4}$ = $\frac{-12}{-4}$ = 3;

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