AP EAMCET · Maths · Complex Number
If \(\alpha\) and \(\beta\) are the roots of the equation \(x^2+x+1\) \(=0\), then the quadratic equation whose roots are \(\alpha^{2023}\) and \(\beta^{1012}\) is
- A \(x^2+x+1=0\)
- B \(x^2-x+1=0\)
- C \(x^2-x+2=0\)
- D \(x^2+x+2=0\)
Answer & Solution
Correct Answer
(A) \(x^2+x+1=0\)
Step-by-step Solution
Detailed explanation
Given : \(\alpha\) and \(\beta\) are roots of the equation \(x^2+x+1=0\) Then \(x=\frac{-1 \pm \sqrt{1-4}}{2}=\frac{-1 \pm \sqrt{3} i}{2}\) \(\therefore \quad \alpha=\frac{-1+\sqrt{3} i}{2}\) and \(\beta=\frac{-1-\sqrt{3} i}{2}\) \(\alpha=-\frac{1}{2}+i \frac{\sqrt{3}}{2}\) and…
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