Question

Find the value of p, for which one of the root of the quadratic equation ${px}^2-14x+8=0is6$ times the other

Answer 1

Let the roots be $\alpha ,6\alpha$

Sum of roots is given as

$\frac{14}{p}=\alpha +6\alpha =7\alpha$

$\alpha =\frac{2}{p}$

$p=\frac{2}{\alpha }$

Product of roots is given as $\frac{8}{p}=6{\alpha }^2$

$⟹p=\frac{4}{3{\alpha }^2}⟹\frac{2}{\alpha }=\frac{4}{3{\alpha }^2}2=\frac{4}{3\alpha }$

$\alpha =\frac{2}{3}$

$⟹p=\frac{2}{\frac{2}{3}}⟹p=3$