Question

If one root of the equation $2x^2-5x+k=0$ be double of the other. Then find the value of $k$.

Answer 1

Let $\alpha$ be one root of the given equation $2x^2-5x+k=0$. Then the other root of the equation will be $2\alpha$.

Then from the relation between the roots and co-efficient we get,

$\alpha +2\alpha =\frac{5}{2}$

or, $\alpha =\frac{5}{6}$.....(1) and $2{\alpha }^2=\frac{k}{2}$ or ${\alpha }^2=\frac{k}{4}$....(2).

Now putting the value of (1) in (2) we get,

$\frac{25}{36}=\frac{k}{4}$

or, $k=\frac{25}{9}$.