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Question: Answered & Verified by Expert
If \( \alpha \) and \( \beta \) are roots of the equation \( \chi^{2}+x+1=0 \) then \( \alpha^{2}+\beta^{2} \) is
MathematicsQuadratic EquationKCETKCET 2019
Options:
  • A \( \frac{-1+i \sqrt{3}}{2} \)
  • B \( -1 \)
  • C \( 11 \)
  • D \( \frac{-1-i \sqrt{3}}{2} \)
Solution:
1950 Upvotes Verified Answer
The correct answer is: \( -1 \)
(B)
$x^{2}+x+1=0$
$\Rightarrow x=\omega, \beta=\omega^{2}$ where $\omega$ is the cube root of unity
$\alpha^{2}+\beta^{2}=\omega^{2}+\omega^{4}$
$=\omega^{2}+\omega$
$=-1$

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