If $\alpha , \beta$  are the roots of the equation $a{x}^2+bx+c=0$then the roots of the equation 

$a{x}^2+b\lambda x+c{\lambda }^2=0$are

If $\alpha , \beta$  are the roots of the equation $f\left(x\right)=a{x}^2+bx+c=0$

then the roots of the equation 

$$\begin{gathered} a{x}^2+b\lambda x+c{\lambda }^2=0 \\ \Rightarrow \frac{a{x}^2}{{\lambda }^2}+\frac{b\lambda x}{{\lambda }^2}+\frac{c{\lambda }^2}{{\lambda }^2}=0 \\ \Rightarrow a{\left(\frac{x}{\lambda }\right)}^2+b\left(\frac{x}{\lambda }\right)+c=0 \\ it is of the form f\left(\frac{x}{\lambda }\right)=0 \end{gathered}$$

the roots of the equation $a{x}^2+b\lambda x+c{\lambda }^2=0$are $\alpha \lambda ,\beta \lambda$