If the sum of the roots of the equation x^{2}-px+q=0 be m times their difference, prove that p^{2}(m^{2}-1)=4m^{2}q

Let the roots of given equation be α and β.

⇒ Sum of roots = α + β = *p* ......(1)

and product of roots = α β = *q* .......(2)

According to the given condition,

Adding (1) and (3), we get

On putting value of α in (3), we get

On putting value of α and β in (2), we get

Hence Proved

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