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Question

α,β are the roots of the equation x2+14x+10=0.
Find the value of (α2 + β2).


A

196

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B

206

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C

186

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D

176

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Solution

The correct option is D

176


Given: α,β are the roots of the equation x2+14x+10=0.
Using the relation between roots and coefficients,
α+β=14 ...(i)
αβ=10 ...(ii)
We know (α+β)2=α2+β2+2αβ
α2 + β2=(α+β)22αβ

α2 + β2=(14)22×10

=19620

=176



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