Question

Розкласти на множники квадратний тричлен.-в^2+2в+24; 4х^2-20х+25;

Answer 1

Ответ:

• $(6 - b)(4 + b) \:$
• $(4x - 10)(x - 2.5) \:$

Объяснение:

$- {b}^{2} + 2 b + 24 = a(b - b_{1})(b - b_{2}) \\ - {b}^{2} + 2 b + 24 = 0 \\ d = 4 + 4 \times 24 = 100 \\ b_{1} = \frac{ - 2 + \sqrt{100} }{ - 2} = \frac{ - 2 + 10}{ - 2} = - 4 \\ b_{2} = \frac{ - 2 - \sqrt{100} }{ - 2} = \frac{ - 2 - 10}{ - 2} = 6 \\ - - - - - - - \\ - {b}^{2} + 2 b + 24 = - (b + 4)(b - 6) = (6 - b)(4 + b)$

$4 {x}^{2} - 20x + 25 = a(x - x_{1})(x - x_{2}) \\ 4 {x}^{2} - 20x + 25 = 0 \\ d = 400 - 4 \times 4 \times 25 = 400 - 400 = 0 \\ x_{1,2} = \frac{20 ± \sqrt{0} }{8} = \frac{5}{2} = 2.5 \: \\ - - - - - - - - \\ 4 {x}^{2} - 20x + 25 = 4(x - 2.5)(x - 2.5) = (4x - 10)(x - 2.5)$