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Question

If α&β are the roots of equation. x2+px+q=0, then - 1α,1β are the roots of the equation.

A

x2px+q=0

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B

x2+px+q=0

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C

qx2+px+1=0

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D

qx2px+1=0

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Solution

The correct option is D

qx2px+1=0


Given equation : x2+px+q=0 Also, α&β are the roots of the given equation. Then, sum of the roots = α+β = -p Now, for roots - 1α,1β, we have : Sum of the roots = - 1α,1β=α+βαβ Hence, the equation involving the roots =(pq)=pq Hence, the equation involving the roots1α,1β is as follows:x2(α+β)x+αβ=0x2pqx+1q=0qx2px+1=0


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