If the sum of the roots of the equation x2-px+q=0 be m times their difference, prove that p2(m2-1)=4m2q

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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