Question

Разложите на множители квадратный трехчлен! а) -x2-3x+10 б) 6x2+5x-4 в) 7x2+20x-3

Answer 1

$ax^2 + bx +c = a(x-x_1)(x-x_2)$

A) -X2-3X+10
$-x^2-3x + 10 \\ D = 3^2 - 4*(-1)*10=49=7^2 \\ \\ x_1 = \frac{3- 7 }{-2} =2 \\ \\ x_2 = \frac{3+7 }{-2} =-5 \\ \\ -x^2-3x + 10= -(x-2)(x+5)$

Б) 6X2+5X-4
$6X^2+5X-4 \\ D = 5^2 - 4*6*(-4)=121 = 11^2 \\ \\ X_1 = \frac{-5+11}{12} = \frac{6}{12} = \frac{1}{2} \\ \\ X_2 = \frac{-5-11}{12} = \frac{-16}{12} = -\frac{4}{3} \\ \\ 6X^2+5X-4 = 6(X - \frac{1}{2} )(X+ \frac{4}{3} )=(2X-1)(3X+4)$

В) 7X2+20X-3
$7X^2+20X-3 \\ \frac{D}{4} = (\frac{b}{2})^2-ac= 10^2-7*(-3)=121=11^2 \\ \\ X_1= \frac{-\frac{b}{2} - \sqrt{ \frac{D}{4} } }{a} = \frac{-10 - 11}{7} =-3 \\ \\ X_2 = \frac{-10+11}{7} = \frac{1}{7} \\ \\ 7X^2+20X-3=7(X+3)(X- \frac{1}{7} )=(X+3)(7X-1)$