Question

If one root of the equation $x^2-px+q=0$ is twice the othere. Prove that $2p^2=9q$.

Answer 1

Let $a$ and $b$ be the roots of the equation $x^2-px+q=0$.

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

$a+b=p$.....(1) and $ab=q$......(2).

According to the problem, $a=2b$. Using this in (1) and (2) we get,

$3b=p$ and $2b^2=q\Rightarrow 2\frac{p^2}{9}=q\Rightarrow 4p^2=9q$ [Using the value of $b$]