Вправи: 814 (1-2)

814. Розкладіть на лінійні множники квадратний тричлен:

1) 2x² – 5x – 3 = 2(x – 32)(x – 1) = (2x – 3)(x – 1);

D = (–5)² – 4 • 2 • 3 = 25 – 24 = 1.

x₁ = 5-12•2 = 5-14 = 44 = 1; x₂ = 5+12•2 = 5+14 = 64 = 32.

2) 5x² + 4x – 1 = 5(x – 15)(x + 1) = (5x – 1)(x + 1);

D = 4² – 4 • 5 • (–1) = 16 + 20 = 36;

x₁ = -4-362•5 = -4-610 = -1010 = –1;

x₂ = -4+362•5 = -4+610 = 210 = 15.

3) –3x² – x + 14 = –3(x + 73)(x – 2) = –(3x + 7)(x – 2);

D = (–1)² – 4 • (–3) • 14 = 1 + 168 = 169.

x₁ = 1-1692•(-3) = 1-13-6 = -12-6 = 2;

x₂ = 1+1692•(-3) = 1+13-6 = 14-6 = –73.

4) 6x² – 5x + 1 = 6(x – 12)(x – 13) = (2x – 1)(3x – 1);

D = (–5)² – 4 • 6 • 1 = 25 – 24 = 1.

x₁ = 5-12•6 = 5-112 = 412 = 13;

x₂ = 5+12•6 = 5+112 = 612 = 12.

5) –9x² + 12x – 4 = –(9x² – 12x + 4) = –(3x – 2)²;

6) 3x² – 8x + 5 = 3(x – 53)(x – 1) = (3x – 5)(x – 1);

D = (–8)² – 4 • 3 • 5 = 64 – 60 = 4;

x₁ = 8-42• 3 = 8-26 = 66 = 1;

x₂ = 8+42• 3 = 8+26 = 106 = 53.

7) 4x² – 4x + 1 = (2x – 1)².

8) –2x² + 3x + 2 = –2(x + 12)(x – 2) = –(2x + 1)(x – 2);

D = 3² – 4 • (–2) • 2 = 9 + 16 = 25.

x₁ = -3-252•(-2) = -3-5-4 = -8-4 = 2;

x₂ = -3+252•(-2) = -3+5-4 = 2-4 = –12.