Задачі і вправи для повторення » 42

42. Розкладіть квадратний тричлен на лінійні множники: 1) x2 – 7x + 12 = (x – 3)(x – 4); D = (–7)2 – 4 • 1 • 12 = 49 – 48 = 1; x1 = (7- √1)/(2 •1) = (7-1)/2 = 6/2 = 3; x2 = (7 + √1)/(2 •1) = (7+1)/2 = 8/2 = 4; 2) x2 + 2x – 35 = (x + 7)(x – 5); x1 + x2 = –2; x1 • x2 = –35; x1 = –7; x2 = 5. 3) 3x2 + 5x + 2 = 3(x + 2/3)(x + 1) = (3x + 2)(x + 1); D = 52 – 4 • 3 • 2 = 25 – 24 = 1; x1 = (-5- √1)/(2 •3) = (-5-1)/6 = (-6)/6 = –1; x2 = (-5 + √1)/(2 •3) = (-5+1)/6 = (-4)/6 = –2/3; 4) –6x2 + 17x – 5 = –6(x – 1/3)(x – 5/2) = –3 (x – 1/3) • 2(x – 5/2) = –(3x – 1)(2x – 5); D = 172 – 4 • (–6) • (–5) = 289 – 120 = 169; x1 = (-17- √169)/(2 •(-6)) = (-17-13)/(-12) = (-30)/(-12) = 5/2; x2 = (-17 + √169)/(2 •(-6)) = (-17+13)/(-12) = (-4)/(-12) = 1/3.