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Question

If roots α,β of the equations x2px+16=0 satisfy the relation α2+β2=9, then write the value of P.


Solution

Since, α,β are the roots of the equation. x2px+16=0α+β=ba=(p)1=Pand α  β=ca=161=16Now,α2+β2=9(α+β)22αβ=9 p22×16=9p29+32p=41

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