Вправи: 829

829. Розв’яжіть рівняння:

1) x² – 5x + 6 = 0;

D = (–5)² – 4 • 1 • 6 =1;

x₁ = 5+ 12 = 5+12 = 3; x₂ = 5- 12 = 5-12 = 2.

2) 2x² + 5x – 3 = 0;

D = (–5)² – 4 • 2 • (–3) = 49; D = 7;

x₁ = -5+ 72 •2 = 24 = 0,5; x₂ = -5- 72 •2 = -124 = –3.

3) 3x² + 5x + 2 = 0;

D = 5² – 4 • 3 • 2 = 1; D = 1;

x₁ = -5+ 12 •3 = -46 = –23; x₂ = -5- 16 = –1.

4) x² + 10x + 25 = 0;

D = 10² – 4 • 1 • 25 = 0;

x = -102 = –5.

5) x² + x – 90 = 0;

D = 1² – 4 • 1 • (–90) = 361; D = 19;

x₁ = -1+ 192 = 182 = 9; x₂ = -1- 192 = -202 = –10.

6) x² – 10x – 24 = 0;

D = (–10)² – 4 • 1 • (–24) = 100 + 96 = 196; D = 14;

x₁ = 10+ 142 = 242 = 12; x₂ = 10 - 142 = -42 = –2.