Question

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

Answer 1

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

⇒${\displaystyle ab{x}^2+b^{2}x-acx-bc=0}$ 

⇒${\displaystyle bx(ax+b)-c(ax+b)=0}$ 

⇒${\displaystyle (bx-c)(ax+b)=0}$ 

⇒${\displaystyle bx-c=0 \text{or} ax+b=0}$ 

⇒${\displaystyle x=\frac{c}{b} \text{or} x=-\frac{b}{a}}$ 

Hence, the roots of the equation are ${\displaystyle \frac{c}{b}}$ and ${\displaystyle -\frac{b}{a}}$