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Question

If α,β are the roots of the equation 2x2+3x+4=0, find αβ+βα


A

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B

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C

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D

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Solution

The correct option is C


α+β=32αβ=42=2αβ+βα=α2+β2αβ=(α+β)22αβαβ=(32)22×22=(944)2=78

Note that even though the numerator was some of squares and the denominator was positive, we got a negative value. This is because the roots of the equation are complex numbers.


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