Відповіді до вправ § 20 - § 26: 24.9 (1-3)

24.9 Розкладіть на множники квадратний тричлен:

1) x² – 5x + 4.

D = (–5)² – 4 • 4 = 9;

x₁ = 5+32 = 5; x₂ = 5-32 = 1;

x² – 5x + 4 = (x – 4)(x – 1).

2) x² + 7x – 8.

D = 7² – 4 • (–8) = 81;

x₁ = -7+92 = 1; x₂ = -7-92 = –8;

x² + 7x – 8 = (x – 1)(x + 8).

3) 2x² – 5x + 2.

D = (–5)² – 4 • 2 • 2 = 9;

x₁ = 5+34 = 2; x₂ = 5-34 = 12;

2x² – 5x + 2 = 2(x – 2)(x – 12) = (x – 2)(2x – 1).

4) –x² + 11x – 24.

11² – 4 • (–1) • (–24) = 25;

x₁ = -11+5-2 = 3; x₂ = -11-5-2 = 8;

–x² + 11x – 24 = –(x – 3)(х – 8) = (3 – x)(x – 8).

5) –3x² + 8х + 3.

D = 8² – 4 • (–3) • 3 = 100;

x₁ = -8+10-6 = –13; x₂ = -8-10-6 = 3;

–3x² + 8x + 3 = –3(x + 13)(x – 3) = (3x + 1)(3 – x).

6) 4x² + x – 3.

D = 1² – 4 • 4 • (–3) = 49;

x₁ = -1+78 = 34; x₂ = -1-78 = –1;

4x² + x – 3 = 4(x – 34)(x + 1) = (4x – 3)(х + 1).