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Question

If ‘α’ and ‘β’ are the zeroes of the quadratic polynomial p(x)=x2+7x+5, then (αβ)2 equals

A
29
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B
49
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C
69
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D
9
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Solution

Given that α and β are zeroes of the quadratic polynomial x2+7x+5.

∴ α + β = –7 and αβ = 5 …..(ii)


Now, (αβ)2=α2+β22αβ

(αβ)2=α2+β2+2αβ4αβ (Adding and subtracting 2αβ on RHS)

(αβ)2=(α+β)24αβ

(αβ)2=(7)24×5=4920=29 [Using (i)]

Hence, the correct answer is option (a).

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