Question

Solve:$ab{x}^2+(b^2-ac)x-bc=0$.

Answer 1

Given: $ab{x}^2+(b^2-ac)x-bc=0$

Factorizing the given equation,

$⟹ab{x}^2+b^{2}x-acx-bc=0$

$⟹bx(ax+b)-c(ax+b)=0$

$⟹(bx-c)(ax+b)=0$

Solving the above equation for $x$, we get

$⟹(bx-c)=0$ or $(ax+b)=0$

$⟹x=\frac{c}{b}$ or $x=\frac{-b}{a}$