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Question

If α and βare the roots of the equationx2-x+1=0, thenα2009+β2009is equal to


A

-2

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B

-1

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C

1

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D

2

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Solution

The correct option is C

1


Explanation for correct option:

Step:1. The given quadratic equation :

Given that α and βare the roots of the equationx2-x+1=0.

(α+β)=1;α.β=1And also

x2x+1=0(x+1)(x2x+1)=0x3+1=0x3=-1.......(i)

Put α,βin equation (i). we get

α3=-1and β3=-1

Step:2. Find the value of α2009+β2009:

Now, α2009+β2009

=α2010α+β2010β=(α3)670α+(β3)670β=(-1)670α+(-1)670β=1α+1β=(α+β)αβ=1

Hence, the correct option is C.


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