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Question

If α and β are the roots of the equation 2x23x5=0, then form a quadratic equation whose roots are α2 and β2.

A
4x229x+25=0
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B
4x2+29+25=0
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C
4x22925=0
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D
None of these
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Solution

The correct option is A 4x229x+25=0
α and β are two roots of the given quadratic equation 2x23x5=0
2x23x5=0
2x25x+2x5=0
x(2x5)+1(2x5)=0
(2x5)(x+1)=0
2x5=0 and x+1=0
x=52 and x=1
α=52 and β=1
α2=(52)2=254
β2=(1)2=1
New roots are 254 and 1.
New quadratic equation,
(x254)(x1)=0
x2x25x4+254=0
4x24x25x+25=0
4x229x+25=0

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