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Question

If the difference between the roots of x2+2px+q=0 be same as that between the roots of x2+2qx+p=0 (pq), then p+q is equal to

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Solution

Let α and β are the roots of the equation x2+2px+q=0 and α and β be the roots of the equation x2+2qx+p=0.

αβ=αβ[Given]

(α+β)24αβ=(α+β)24αβ

(2p)24q=(2q)24p

4p24q2=4q4p

p2q2=qp

(pq)(p+q)=(pq)

p+q=1

Hence, value of p+q is equal to 1.

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