Вправи: 728

728. Розкладіть на лінійні множники квадратний тричлен:

1) х² – 7x + 12 = (х – 3)(х – 4); х² – 7х + 12 = 0,

х₁ = 3, х₂ = 4;

2) х² + 8х + 15 = (х + 3)(х + 5); х² + 8х + 15 = 0,

х₁ = –3, х₂ = –5;

3) х² – Зх – 10 = (х – 5)(х + 2); х² – Зх – 10 = 0,

х₁ = 5, х₂ = –2;

4) –х2 – 5х – 6 = –(x + 2)(х + 3); –х2 – 5х – 6 = 0;

х² + 5х + 6 = 0, х₁ = –2, х₂ = –3;

5) –х² + х + 2 = –(х – 2)(x + 1); –х² + х + 2 = 0;

х² – х – 2 = 0, х₁ = 2, х₂ = –1;

6) 6x² – 5х – 1 = 6(х – 1)(x + 16) = (x – 1)(6x + 1);

6x² – 5x – 1 = 0; D = 25 + 24 = 49,

x₁ = 5+712 = 1, x₂ = 5-712 = –16;

7) 4x² + 3x – 22 = 4(x – 2)(x + 114) = (x – 2)(4x + 11);

4x² + 3 + x – 22 = 0; D = 9 + 352 = 361, D = 19;

x₁ = -3+198 = 2, x₂ = -3-198 = –228 = –114;

8) –3a² + 8a + 3 = 3(a + 13)(a – 3) = –(3a + 1)(a – 3);

–3a² + 8a + 3 = 0; 3a² – 8a – 3 = 0;

D₁ = 16 + 9 = 25; D1 = 5;

a₁ = 4+53 = 3, a₂ = 4-53 = –13;

9) 16b² – 56b + 1 = 16(b – 3)(b – 2); 16b² – 56b + 1 = 0;

b² – 5b + 6 = 0; b₁ = 3, b₂ = 2;

10) –2x² – 0,5x + 1,5 = –2(x – 34)(x + 1);

–2x² – 0,5x + 1,5 = 0; 4x² + x – 3 = 0; D = 1 + 48 = 49,

D = 7; x₁ = -1+78 = 68 = 34, x₂ = -1-78 = –1;

11) 0,4х² – 2х + 2,5 = 0,4(х – 2,5)(х – 2,5) = (0,2х – 0,5)(0,2х – 0,5) = (0,2х – 0,5)²; 0,4х² – 2х + 2,5 = 0;

4х² – 20х + 25 = 0; D₁ = 100 – 100 = 0; x = 208 = 52 = 2,5;

12) –1,2m² + 2,6m – 1 = –1,2(m – 12)(m + 53);

–1,2m² + 2,6n – 1 = 0; 1,2m² – 2,6m + 1 = 0;

12m² + 26m + 10 = 0; 6m² – 13m + 5 = 0;

D = 169 – 120 = 49, D = 7;

m₁ = 13-712 = 612 = 12, m₂ = -13-712 = -2012 = –53.