AP EAMCET · Maths · Complex Number
If \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-x+1=0\), then \(\alpha^{2009}+\beta^{2009}\) is equal to
- A -2
- B -1
- C 1
- D 2
Answer & Solution
Correct Answer
(C) 1
Step-by-step Solution
Detailed explanation
\(\alpha\) and \(\beta\) are the roots of quadratic equation \[ \begin{aligned} x^2-x+1 & =0 \\ x^2-x+1 & =0 \\ x & =\frac{1 \pm \sqrt{1-4}}{2}=\frac{1 \pm \sqrt{-3}}{2} \\ & =\frac{1 \pm \sqrt{3} i}{2}=-\omega \text { and }-\omega^2 \end{aligned} \] [where, \(w\) is cube roots…
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