ГДЗ Алгебра 9 клас Істер НУШ

68. Розкладіть на множники квадратний тричлен:

1) x2 – 5x – 6 = (x + 1)(x – 6);
x1 + x2 = 5;
x1 • x2 = –6; x1 = –1; x2 = 6.
2) 3x2 – 4x + 1 = 3(x – 1/3)(x – 1) = (3x – 1)(x – 1);
D = (–4)2 – 4 • 3 • 1 = 16 – 12 = 4.
x1 = (4 -√4 )/(2 • 3) = (4 - 2)/6 = 2/6 = 1/3;
x2 = (4 + √4)/(2 • 3) = (4 + 2)/6 = 6/6 = 1.
3) –2x2 + 7x – 3 = –2(x – 1/2)(x – 3) = (–2x + 1)(x – 3) = (1 – 2x)(x – 3).
D = 72 – 4 • (–2) • (–3) = 49 – 24 = 25.
x1 = (-7 -√25)/(2 • (-2)) = (-7 -5)/(-4) = (-12)/(-4) = 3;
x2 = (-5 + 5)/(-4) = (-2)/(-4) = 1/2.