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Question

If the sum of the roots of quadratic equation ax2+bx+c=0 is equal to the sum of the squares of their reciprocal then
ac,ba,cb, are in

A
G.P.
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B
H.P.
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C
A.G.P.
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D
A.P.
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Solution

The correct option is B H.P.
It is given that
α+β=1α2+1β2

=(α+β)22α.βα2.β2
ba=b22acc2
bc2=ab22a2c
2a2c=ab2+bc2
Dividing the entire equation by abc, we get
2ab=bc+ca
Hence
bc,abca are in A.P.
Hence their reciprocals will be in H.P.

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