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Question

If c0 and α,β are the roots of the quadratic equation ax2+bx+c=0, then value of aα2+caα+b+aβ2+caβ+b is

A
b(b22ac)4a
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B
(b22ac)2a
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C
b(b22ac)a2c
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D
b(b22ac)ac
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Solution

The correct option is C b(b22ac)a2c
aα2+bα+c=0
aα2+c=bα
aα2+bα=c
aα+b=cα
aα2+caα+b=bcα2
Similarly, aβ2+caβ+b=bcβ2aα2+caα+b+aβ2+caβ+b=bc(α2+β2)=bc(b2a22ca)
=(b22ac)ba2c

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