Вправи: 413 (1-3)

413. Знайдіть нулі квадратичної функції:

1) у = х² + 4х – 5;

х² + 4х – 5 = 0;

D = 16 + 4 • 5 = 36; x_1,2 = -4 ±62;

x₁ = -4+62 = 22 = 1; x₂ = -4- 62 = -102 = –5.

2) y = x² – 7x – 8;

x² – 7x – 8 = 0;

D = 49 + 48 = 81;

x_1,2 = 7 ± 92; x₁ = 8; x₂ = –1

3) y = –6x² – x + 1;

–6x² – x + 1 = 0;

D = 1 + 4 • 1 • 6 = 1 + 24 = 25;

x_1,2 = –1 ±52 •6; x₁ = -1+512 = 412 = 13; x₂ = -1-512 = -612 = –12.

4) y = 2x² – 11x + 5; 2x² – 11x + 5 = 0;

D = 121 – 4 • 2 • 5 = 121 – 40 = 81;

x_1,2 = 11 ±92 •2; x₁ = 11+94 = 204 = 5; x₂ = 11-94 = 24 = 12.

5) y = 2x² – 5x + 3;

2x² – 5x + 3 = 0;

D = 25 – 4 • 2 • 3 = 25 – 24 = 1;

x_1,2 = 5 ± 14; x₁ = 64 = 32; x₂ = 44 = 1.

6) y = 4x² – 4x + 1;

4x² – 4x + 1 = 0;

D = 16 – 4 • 1 • 4 = 16 – 16 = 0;

x_1,2 = 4 ±024 = 48 = 12.

7) y = 4x² – x – 3;

4x² – x – 3 = 0;

D = 1 + 4 • 3 • 4 = 1 + 48 = 49;

x_1,2 = 1 ± 78; x₁ = 1; x₂ = -68 = –34.

8) y = 5x² + 14x – 3;

5x² + 14x – 3 = 0;

D = 14² + 4 • 5 • 3 = 196 + 60 = 256;

x_1,2 = -14 ±162 •5 = -14±1610;

x₁ = -3010 = –3; x₂ = 210 = 15.