Question

If one root of equation $x^2-px+q=0$ is twice the other then prove that ${2p}^2=9q$

Answer 1

Let ß is one root and 2ß is 2nd root

$x^2-px+q=0$ so,

The sum of the roots$=P$

$ß+2ß=P$

$ß=\frac{P}{3}$ ---(1)

The product of the roots $=q$

$2ß.ß=q$

$2{ß}^2=q$

put eqn (1)

$2(\frac{P}{3}{)}^2=q$

$2P^2=9q$