TS EAMCET · Maths · Complex Number
If \(\omega\) is a complex cube root of unity and \(x=\omega^2-\omega+2\) then
- A \(x^2-4 x+7=0\)
- B \(x^2+4 x+7=0\)
- C \(x^2-2 x+4=0\)
- D \(x^2+2 x+4=0\)
Answer & Solution
Correct Answer
(A) \(x^2-4 x+7=0\)
Step-by-step Solution
Detailed explanation
\(\omega^2 = -1 - \omega\) \(x = (-1-\omega) - \omega + 2\) \(x = 1 - 2\omega\) \(2\omega = 1 - x\) \(\omega = \frac{1-x}{2}\) \(1 + \frac{1-x}{2} + \left(\frac{1-x}{2}\right)^2 = 0\) \(4 + 2(1-x) + (1-x)^2 = 0\) \(4 + 2 - 2x + 1 - 2x + x^2 = 0\) \(x^2 - 4x + 7 = 0\)
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