Вправи: 815

815. Розкладіть на лінійні множники квадратний тричлен.

1) 3x² + 5x – 2 = 3(x – 13)(x + 2) = (3x – 1)(x + 2);

D = 5² – 4 • 3 • (–2) = 25 + 24 = 49.

x₁ = -5-492•3 = -5-76 = -126 = –2;

x₂ = -5+492•3 = -5+76 = 26 = 13.

2) –2x² + x + 15 = –2(x + 52)(x – 3) = –(2x + 5)(x – 3);

D = 1² – 4 • (–2) • 15 = 1 + 120 = 121.

x₁ = -1-1212•(-2) = -1-11-4 = -12-4 = 3;

x₂ = -1+1212•(-2) = -1+11-4 = 10-4 = –52.

3) 9x² + 6x + 1 = (3х + 1)².

4) –5x² + 6x – 1 = –5(x – 15)(x – 1) = –(5x – 1)(x – 1);

D = 6² – 4 • (–5) • (–1) = 36 – 20 = 16.

x₁ = -6-162•(-5) = -6-4-10 = -10-10 = 1;

x₂ = -6+162•(-5) = -6+4-10 = -2-10 = 15.