§ 4: 4.15

4.15 Розкладіть на множники квадратний тричлен:

1) х² + х – 6 = 0; х² + х – 6 = (х + 3)(х – 2);

х₁ + х₂ = –1, х = –3,

х₁ • х₂ = –6; х = 2

2) 35 – 2х – х² = 0; х² + 2х – 35 = 0;

х² + 2х – 35 = –(–х²–2х + 35) = –(х + 7)(х – 5);

х₁ + х₂ = –2, х = –7,

х₁ • х₂ = –35; х = 5;

3) 2х² + 9х – 18 = 0; D = 81 – 4 • 2 • (–18) = 81 + 154 = 225;

x₁ = -9+154 = 64 = 32;

x₂ = -9-154 = -244 = –6; 2x² + 9x – 18 = 2(x – 32)(x + 6) = (2x – 3)(x + 6);

4) х² – 16х + 3 = 0; D = 16² – 4 • 5 • 3 = 256 – 60 = 196;

x₁ = 16-1410 = 210 = 15; x₂ = 16+ 1410 = 3; 5x² – 16x + 3 = 5(x – 15)(x – 3) = = (5x – 1)(x – 3).