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Question

If α,β & γ are the roots of the equation x3x1=0 then the value of, 1+α1α+1+β1β+1+γ1γ is

A
Zero
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B
1
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C
7
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D
1
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Solution

The correct option is D 1

We have,

Cubic equation is x3x1=0

Now, we can written as,

x3+0x2x1=0

Roots are α,βandγ

Then,

Sum of roots =coeff.ofx2coeff.ofx3

α+β+γ=01

α+β+γ=0......(1)

Both product of roots=coeff.ofxcoeff.ofx3

αβ+βγ+γα=11

αβ+βγ+γα=1......(2)


Product of roots=constanttermcoeff.ofx3

αβγ=11

αβγ=1......(3)


From equation (1), (2) and (3) to and we get,

α=1,β=1,γ=0

Then,


According to question,

1+α1α+1+β1β+1+γ1γ

1+111+111+1+1+010

1


Hence, this is he answer.


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