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Question

If the sum of the roots of the equation ax2+bx+c=0 is equal to the sum of the squares of their reciprocals, then b2ac+bca2=


A

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B

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C

0

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D

3

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Solution

The correct option is A

2


x1+x2=ba, x1x2=ca1x21+1x22=x21+x22x21x22=(x1+x2)22x1x2(x1x2)2=(x1+x2x1x2)22x1x2=b2c22acNow, b2c22ac=ba ...(Given) b2c2acc=bcab2ac2=bca2b2ac+bca2=2


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