Найдите корни квадратных трехчленов и разложите их на множители: 1) x^+12x+27 2) 3x^+15x-183) 9x^-12x+44) 15x^+13x+3

1) f (x) = x^2 + 12x + 27;

D/4 = 6^2 - 27 = 36 - 27 = 9; x = - 6 ± √9 = - 6 ± 3; x1 = - 6 - 3 = - 9; x2 = - 6 + 3 = - 3; f (x) = (x + 9) (x + 3).

2) g (x) = 3x^2 + 15x - 18;

D = 15^2 + 4 * 3 * 18 = 225 + 216 = 441; x = (-15 ± √441) / 6 = (-15 ± 21) / 6; x1 = (-15 - 21) / 6 = - 36/6 = - 6; x2 = (-15 + 21) = 6/6 = 1; g (x) = 3 (x + 6) (x - 1).

3) u (x) = 9x^2 - 12x + 4;

D/4 = 6^2 - 9 * 4 = 0; x1 = x2 = 6/9 = 2/3; u (x) = 9 (x - 2/3) ^2 = (3x - 2) ^2.

4) v (x) = 15x^2 + 13x + 3;

D = 13^2 - 4 * 15 * 3 = 169 - 180 = - 11 < 0.

Нет действительных корней.