WBJEE · Maths · Quadratic Equation
If \(\alpha\) and \(\beta\) are the roots of the equation \(x^2+x+1=0\), then the equation whose roots are \(\alpha^{19}\) and \(\beta^7\) is
- A \(x^2-x-1=0\)
- B \(x^2-x+1=0\)
- C \(x^2+x-1=0\)
- D \(x^2+x+1=0\)
Answer & Solution
Correct Answer
(D) \(x^2+x+1=0\)
Step-by-step Solution
Detailed explanation
Hints: \(\alpha\) and \(\beta\) are the roots of \(x^2+x+1=0\) \(\begin{array}{ll} \alpha=\omega & \beta=\omega^2 \\ \alpha^{19}=\omega & \beta^7=\omega^2 \\ x^2-\left(\alpha^{19}+\beta^7\right) x+\alpha^{19} \beta^7=0 \end{array}\) Thou,…
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