AP EAMCET · Maths · Complex Number
If \(\alpha\) is a non-real root of the equation \(x^6-1=0\) then \(\frac{\alpha^2+\alpha^3+\alpha^4+\alpha^5}{\alpha+1}=\)
- A \(\alpha\)
- B 1
- C 0
- D \(-1\)
Answer & Solution
Correct Answer
(D) \(-1\)
Step-by-step Solution
Detailed explanation
\(\alpha^6=1\) \(\alpha^5+\alpha^4+\alpha^3+\alpha^2+\alpha+1=0\) \(\alpha^2+\alpha^3+\alpha^4+\alpha^5 = -(\alpha+1)\) \(\frac{-(\alpha+1)}{\alpha+1}=-1\)
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