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Question

If α and β are the roots of the equation 3x2+2x+1=0, then the equation whose roots are α+β1 and β+α1 is

A
3x2+8x+16=0
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B
3x28x16=0
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C
3x2+8x16=0
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D
x2+8x+16=0
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Solution

The correct option is D 3x2+8x+16=0
Sum of the roots of the equation 3x2+2x+1=0
Sum of the roots α+β=23
Product of the roots αβ=13
Sum of the roots of unknown equation α+1β+β+1α

=(α+β)+(1α+1β)
=(α+β)+(α+βαβ)
=23+2313
=23283

Product of the roots (α+1β)(β+1α)

=αβ+α.1α+β.1β+1αβ

Substituting αβ=13

=13+2+113

=163

The general form of quadratic equation is x2(sum of the roots)x+Product of the roots=0

Substituting the respective values, we get
x2(83)x+163=0

Multiplying by 3 on both sides, we get
3x2+8x+16=0

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