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Question

If α,β are the roots of 2x2+5x+1=0, then the equation whose roots are 2α+1,2β+1 is

A
x23x2=0
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B
x2+3x2=0
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C
x2+3x+2=0
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D
x23x+2=0
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Solution

The correct option is B x2+3x2=0
f(x)=2x2+5x+1=0α,β are the roots.
Let y=2x+1, where x=α,β
x=y12
The equation whose roots are 2α+1,2β+1 is,
f(x12)=0
2(x1)24+5(x1)2+1=0
(x1)2+5(x1)+2=0x2+3x2=0

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