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Question

If α and β be the roots of the equation 2x2+2(a+b)x+a2+b2=0, then the equation whose roots are (α+β)2 and (αβ)2) is


A

x22abx(a2b2)2=0

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B

x24abx(a2b2)2=0

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C

x24abx+(a2b2)2=0

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D

None of these

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Solution

The correct option is B

x24abx(a2b2)2=0


Sum of roots α + β = -(a + b) and αβ = a2+b22

(α+β)2=(a+b)2 and (αβ)2=α2+β22αβ

=2ab(a2+b2)=(ab)2

Now the required equation whose roots are

(α+β)2 and (αβ)2

x2{(α+β)2+(αβ)2}x+(α+β)2(αβ)2=0

x2{(a+b)2+(ab)2}x+(a+b)2(ab)2=0

x24abx(a2b2)2=0


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