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Question

If the sum of the roots of the quadratic equation a2+bx+c=0 is equal to the sum of the squares of their reciprocals, then ac,ba,cb are in

A
A.P.
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B
G.P.
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C
H.P.
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D
None of these
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Solution

The correct option is C H.P.

As given , if α,β be the roots of the quadratic equation, then
α+β=1α2+1β2=(α+β)22αβα2β2
ba=(b2a2)(2ca)(c2a2)=b22acc2
2ac=b2c2+ba=(ab2+bc2)ac2
2a2c=ab2+bc22ab=bc+ca
ca,ab,bc are in A.Pac,ba,cb are in H.P.


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