Question

If one root of the quadratic equation $k{x}^2-14x+8=0$ is six times the other, find the value of $k$.

Answer 1

Let the roots of the equation be $k{x}^2-5x+2=0$, $\alpha$ and $4\alpha$
Then, sum of the roots, $\alpha +4\alpha =\frac{5}{k}$,

$\Rightarrow \alpha =\frac{1}{k}$ ......(1)
Product of roots, $\alpha .4\alpha =\frac{2}{k}$
$4(\frac{1}{k}{)}^2=\frac{2}{k}$ ........From (1)

$\therefore k=2$