Разложить квадратный трехчлен на множители:1) x - 2x - 48; 2)

Квадратный трехчлен раскладывается на множители по формуле ax^2 + bx + c = a(x - x1)(x - x2), где х1 и х2 - корешки квадратного трехчлена.

1) x^2 - 2x - 48 = 0;

D = b^2 - 4ac;

D = (-2)^2 - 4 * 1 * (-48) = 4 + 192 = 196; D = 14;

x = (-b  D)/(2a);

x1 = (2 + 14)/2 = 16/2 = 8;

x2 = (2 - 14)/2 = - 12/2 = -6;

x^2 - 2x - 48 (x - 8)(x + 6).

2) 2x^2 - 5x + 3 = 0;

D = (-5)^2 - 4 * 2 * 3 = 25 + 24 = 49; D = 7;

x1 = (5 + 7)/4 = 12/4 = 3;

x2 = (5 - 7)/4 = -2/4 = -0,5;

2x^2 - 5x + 3 = 2(x + 0,5)(x - 3) = (2x + 1)(x - 3).

3) 3x^2 - 10x + 3 = 0;

D = (-10)^2 - 4 * 3 * 3 = 100 - 36 = 64; D = 8;

x1 = (10 + 8)/6 = 18/6 = 3;

x2 = (10 - 8)/6 = 2/6 = 1/3;

3x^2 - 10x + 3 = 3(x - 1/3)(x - 3) = (3x - 1)(x - 3).

4) 5x^2 - x - 42 = 0;

D = (-1)^2 - 4 * 5 * (-42) = 1 + 840 = 841; D = 29;

x1 = (1 + 29)/10 = 30/10 = 3;

x2 = (1 - 29)/10 = -28/10 = -2,8;

5x^2 - x - 42 = 5(x + 2,8)(x - 3) = (5x +14)(x - 3).

5) 3x^2 - 8x + 5 = 0;

D = (-8)^2 - 4 * 3 * 5 = 64 - 60 = 4; D = 2;

x1 = (8 + 2)/6 = 10/6 = 5/3;

x2 = (8 - 2)/6 = 6/6 = 1;

3x^2 -8x + 5 = 3(x - 5/3)(x - 1) = (3x - 5)(x - 1).

6) 36x^2 - 12x + 1 = 0;

D = (-12)^2 - 4 * 36 * 1 = 144 - 144 = 0;

x1 = x2 = 12/72 = 1/6;

36x^2 - 12x + 1 = 36(x - 1/6)(x - 1/6) = 6(x - 1/6) * 6(x - 1/6) = (6x - 1)(6x - 1).