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Question

If α,β are the roots of the equation 2x23x6=0, then the equation whose roots are α21 and β21 is

A
2x225x7=0
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B
4x225x+7=0
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C
2x217x+7=0
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D
4x217x+7=0
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Solution

The correct option is B 4x225x+7=0
Let α21=yα=±y+1

Now, α is the root of the equation 2x23x6=0, so
2α23α6=0
2(±y+1)23(±y+1)6=0
2y+26=(±3y+1)
2y4=(±3y+1)
Squaring on both sides, we get
4y216y+16=9(y+1)
4y225y+7=0

Hence, the required equation is 4x225x+7=0



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