Вправи: 729

729. Розкладіть на лінійні множники квадратний тричлен:

1) x² – 3x – 18 = (x – 6)(x + 3); x² – 3x – 18 = 0;

D = 9 + 72 = 81; D = 9; x₁ = 3+92 = 6 або x₂ = 3-92 = –3;

2) x² + 5x – 14 = (x + 7)(x – 2); x² + 5x – 14 = 0;

D = 25 + 36 = 81; D = 9;

x₁ = -5+92 = 2 або x₂ = -5-92 = –7;

3) –x² + 3x + 4 = –(x – 4)(x + 1) = (4 – x)(x + 1);

x² – 3x – 4 = 0; D = 9 + 16 = 25; D = 5;

x₁ = 3+52 = 4 або x₂ = 3-52 = –1;

4) 5x² + 8x – 4 = 5(x – 0,4)(x + 2) = (5x – 2)(x + 2);

5x² + 8x – 4 = 0; D = 64 + 80 = 144; D = 12;

x₁ = -8+1210 = 0,4 або x₂ = -8-1210 = –2;

5) 2a² – 3a + 1 = 2(a – 1)(a – 1)(a – 12) = (a – 1)(2a – 1);

2a² – 3a + 1 = 0; D = 9 – 8 = 1; D = 1;

a₁ = 3+14 = 1 або a₂ = 3-14 = 12;

6) 4b² – 11b – 3 = 4(b – 3)(b + 14) = (b – 3)(4b + 1);

4b² – 11b – 3 = 0; D = 121 + 48 = 169; D = 13;

b₁ = 11+138 = 3 або b₂ = 11-138 = -28 = –14;

7) –14x² – 2x – 3 = –14(x + 2)(x + 6); 14x² + 2x + 3 = 0;

x² + 8x + 12 = 0; D₁ = 16 – 12 = 4; D1 = 2;

x₁ = –4 + 2 = –2 або x₂ = –4 – 2 = –6;

8) 0,3m² – 3m + 7,5 = 0,3(m – 5)(m – 5) = 0,3(m – 2,5)²; 0,3m² – 3m + 7,5 = 0; D = 9 – 9 = 0; m = 30,6 = 5;

9) x² – 2x – 2 = (x – 1 – 3)(x – 1 + 3); x² – 2x – 2 = 0;

D = 4 + 6 = 12; D = 12 = 23;

x₁ = 2+232 = 2(1+ 3)2 = 1 ± 3 або х₂ = 1 – 3.