Вправи: 812 (1-2)

812. Розкладіть на лінійні множники квадратний тричлен.

1) x² – 3x – 10 = (x + 2)(x – 5);

D = (–3)² – 4 • 1 • (–10) = 9 + 40 = 49.

x₁ = 3-492•1 = 3-72 = -42 = –2;

x₂ = 3+492•1 = 3+72 = 102 = 5.

2) x² – 10x + 24 = (x – 4)(x – 6);

D = (–10)² – 4 • 1 • 24 = 100 – 96 = 4.

x₁ = 10-42•1 = 10-22 = 82 = 4;

x₂ = 10+42•1 = 10+22 = 122 = 6.

3) –x² + 16x – 15 = –(x – 15)(x – 1);

D = 16² – 4 • (–1) • (–15) = 256 + 60 = 196.

x₁ = -16-1962•(-1) = -16-14-2 = -30-2 = 15;

x₂ = -16+1962•(-1) = -16+14-2 = -2-2 = 1.

4) x² – 2x – 15 = (x + 3)(x – 5);

D = (–2)² – 4 • 1 • (–15) = 4 + 60 = 64.

x₁ = 2-642•1 = 2-72 = -62 = –3;

x₂ = 2+642•1 = 2+82•1 = 102 = 5.

5) –x² + 4x – 3 = –(x – 1)(x – 3);

D = 4² – 4 • (–1) • (–3) = 16 – 12 = 4.

x₁ = -4-42•(-1( = -4-2-2 = -6-2 = 3;

x₂ = -4+42•(-1) = -4+2-2 = -2-2 = 1.

6) x² – 6x – 7 = (x + 1)(x – 7);

D = (–6)² – 4 • 1 • (–7) = 36 + 28 = 64.

x₁ = 6-642•1 = 6-82 = -22 = –1;

x₂ = 6+642•1 = 6+82 = 142 = 7.

7) x² + 4x + 4 = (x + 2)²;

8) –x² + 10x – 25 = –(x² – 10x + 25) = –(x – 5)².