JEE Mains · Maths · STD 11 - 4.1 complex nubers
The sum of \(162^{\text {th }}\) power of the roots of the equation \(x^{3}-2 x^{2}+2 x-1=0\) is
- A \(2\)
- B \(9\)
- C \(3\)
- D \(6\)
Answer & Solution
Correct Answer
(C) \(3\)
Step-by-step Solution
Detailed explanation
\(x^{3}-2 x^{2}+2 x-1=0\) \(x =1\) satisfying the equation \(\therefore x-1\) is factor of \(x^{3}-2 x^{2}+2 x-1\) \(=(x-1)\left(x^{2}-x+1\right)=0\) \(x=1, \frac{1+i \sqrt{3}}{2}, \frac{1-i \sqrt{3}}{2}\) \(x=1,-\omega^{2},-\omega\) sum of \(162^{\text {th }}\) power of roots…
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