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Question

If α,β are the roots of 2x23x+4=0, then the equation whose roots are α2 and β2 is

A
4x27x16=0
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B
4x27x+16=0
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C
4x2+7x+16=0
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D
4x2+7x16=0
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Solution

The correct option is C 4x2+7x+16=0
Let f(x)=2x23x+4=0 roots are α,β
The equation whose roots are α2,β2 is f(x)=0
2x3x+4=02x+4=3x
(2x+4)2=9x4x2+7x+16=0

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