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Question

Let α,β be the roots of the quadratic equation 3x2+10x+2=0, then the quadratic equation whose roots are αα+5,ββ+5, is

A
46x2+27x+2=0
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B
27x2+2x+48=0
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C
27x2+48x+2=0
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D
27x2+46x+2=0
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Solution

The correct option is D 27x2+46x+2=0
Let y=xx+5, where x=α,β
xy+5y=xx=5y1y
Putting x=5y1y in the quadratic equation
3x2+10x+2=03(5y1y)2+10(5y1y)+2=075y2+50y(1y)+2(1y)2=027y2+46y+2=0

Hence, the quadratic equation whose roots are αα+5,ββ+5 is
27x2+46x+2=0

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