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Question

The sum of the roots of quadratic equation ax2+bx+c=0(a,b,0) is equal to the sum of squares of their reciprocals, then ac,ba and cb are in

A
AP
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B
GP
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C
HP
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D
None of these
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Solution

The correct option is B HP
Given, equation is ax2+bx+c=0
If α and β be the roots of this equation.
Then, according to question
α+β=1α2+1β2=α2+β2α2β2
=(α+β)22αβα2β2
ba=b22acc2
ba=b2c2+ba=ab2+bc2ac2
2a2c=ab2+bc2
2ab+bc+ca
Here ca,ab and bc are in AP.
Therefore, ca,ba and cb are in HP.

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