$$\begin{gathered} If \alpha , \beta are the roots of the equation a{x}^2+bx+c=0, \\ then the quadratic equation whose roots are \alpha +\beta , \alpha \beta is \end{gathered}$$

$$\begin{gathered} \alpha +\beta =\frac{-b}{a} \alpha \beta =\frac{c}{a} \\ (\alpha +\beta )+ \left(\alpha \beta \right) =-\frac{b}{a}+\frac{c}{a}\Rightarrow \frac{(c-b)}{a} \\ \left(\alpha \beta \right)(\alpha +\beta )=\left(\frac{c}{a}\right)\left(\frac{-b}{a}\right)=\left(\frac{-bc}{a^2}\right) \\ \therefore Required equation x^2+\left(\frac{b-c}{a}\right)x-\frac{bc}{a^2}=0 \\ a^2{x}^2+a(b-c)x-bc=0 \end{gathered}$$