ГДЗ Алгебра 9 клас Істер НУШ

67. Розкладіть на множники квадратний тричлен:

1) x2 – 7x + 6 = (x – 1)(x – 6); x1 + x2 = 7;
x1 • x2 = 6; x1 = 1; x2 = 6.
2) 2x2 + 5x + 2 = 2(x + 1/2)(x + 2) = (2x + 1)(x + 2).
D = 52 – 4 • 2 • 2 = 25 – 16 = 9.
x1 = (-5 - √9)/(2 • 2) = (-5 - 3)/4 = (-8)/4 = –2;
x2 = (-5 + 3)/4 = (-2)/4 = –1/2.
3) –3x2 – 5x + 2 = –3(x – 1/3)(x + 2) = (–3x + 1)(x + 2);
D = (–5)2 – 4 • (–3) • 2 = 25 + 24 = 49;
x1 = (5 - √49)/(2 • (-3)) = (5 - 7)/(-6) = (-2)/(-6) = 1/3;
x2 = (5 + 7)/(-6) = 12/(-6) = –2.