Question

Find the value of $\mu$ for which one root of the quadratic equation $\mu x^2-14x+8=0$ in 6 times the other.

Answer 1

Let one root be $\alpha$ other is $6\alpha$

$7\alpha =\frac{14}{\mu }$

$\left(6\alpha \right)\alpha =\frac{8}{\mu }$

$6{\alpha }^2=\frac{8}{\mu }$

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

$6\times \frac{4}{{\mu }^2}=\frac{8}{\mu }$

$\mu =3$

$D>0$ for $\mu =3$ $\therefore \mu =3$ is valid.