Question

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

Answer 1

$$\begin{gathered} \text{Given:} \\ ab{x}^2+(b^2-ac)x-bc=0 \\ \Rightarrow ab{x}^2+b^{2}x-acx-bc=0 \\ \Rightarrow bx(ax+b)-c(ax+b)=0 \\ \Rightarrow (bx-c)(ax+b)=0 \\ \Rightarrow bx-c=0\text{or}ax+b=0 \\ \Rightarrow x=\frac{c}{b}\text{or}x=\frac{-b}{a} \\ \mathrm{H}\text{ence, the roots of the equation are}\frac{c}{b}\text{and}\frac{-b}{a}. \end{gathered}$$