If alpha and beta are the roots of a quadratic equation px^2+qx+q=0, prove that sqrt(alpha/beta)+sqrt(beta/alpha)+sqrt(q/p)=0?

If alpha and beta are the roots of a quadratic equation px^2+qx+q=0, prove that sqrt(alpha/beta)+sqrt(beta/alpha)+sqrt(q/p)=0

1 Answer
Apr 9, 2018

Please see below.

Explanation:

As alpha andbeta are roots of px^2+qx+q=0,

we have alpha+beta=-q/p and alphabeta=q/p

Hence sqrt(alpha/beta)+sqrt(beta/alpha)+sqrt(q/p)

= sqrtalpha/sqrtbeta+sqrtbeta/sqrtalpha+sqrt(q/p)

= (alpha+beta)/sqrt(alphabeta)+sqrt(q/p)

= (-q/p)/sqrt(q/p)+sqrt(q/p)

= -sqrt(q/p)+sqrt(q/p)

= 0