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Question

If α,β are the roots of the equation 3x2+5x+4=0, then the quadratic equation whose roots are α2,β2.


A

9x2+x+16=0

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B

9x2x+16=0

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C

9x2x+24=0

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D

9x2+x+24=0

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Solution

The correct option is B

9x2x+16=0


α+β=53, αβ=43

To find the equation whose roots are α2,β2, we have to find α2+β2 and α2β2

α2+β2=(α+β)22αβ =2592×43 =19α2β2=169
The equation is :
x219x+169=0
9x2x+16=0


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