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Question

Find the equation whose roots are reciprocals of the roots of 2x2+5x+4=0 .


A

5x2+4x+2=0

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B

4x2+5x+2=0

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C

4x2+2x+5=0

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D

2x2+4x+5=0

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Solution

The correct option is B

4x2+5x+2=0


To get the equation whose roots are reciprocals, replace x by 1x.

2×1x2+5x+4=0

Multiplying by x2, ( x0)

2+5x+4x2=0 or 4x2+5x+2=0


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