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Question

The sum of roots of the equation ax2+bx+c=0 is equal to the sum of squares of their reciprocals. Then bc2,ca2andab2 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 AP
Let α,β are roots of ax2+bx+c=0
Then β+α=ba;αβ=ca
Now
β+α=1α2+1β2=β2+α2α2β2=(β+α)22αβα2β2

ba=(ba)22ca(ca)2ba=b22ac(c)2

bc2=ab22ca22a2c=ab2+bc2
So ab2,a2c,bc2 are in A.P

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