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Question

If α, β are the roots of the equation x² – px + q = 0, then the value of α2+β2+2αβ is 

A p² Correct Answer Incorrect Answer
B q² Correct Answer Incorrect Answer
C 1/p² Correct Answer Incorrect Answer
D 2p² Correct Answer Incorrect Answer
E none of these Correct Answer Incorrect Answer

Solution

α, β are the roots of the equation x² – px + q = 0 On comparing the given equation to ax² – bx + c = 0 Here a = 1, b = -p and c = q Therefore, sum of the roots = α + β = -(-p/1) = p Product of the roots = αβ = c/a = q/1 = q now, α2+ β2 + 2αβ = (α + β)2 = p2

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