WBJEE · Maths · Quadratic Equation
If \(\alpha, \beta\) be the roots of the quadratic equation \(\mathrm{x}^2+\mathrm{x}+1=0\) then the equation whose roots are \(\alpha^{19}, \beta^7\) is
- A \(\mathrm{x}^2-\mathrm{x}+1=0\)
- B \(\mathrm{x}^2-\mathrm{x}-1=0\)
- C \(\mathrm{x}^2+\mathrm{x}-1=0\)
- D \(x^2+x+1=0\)
Answer & Solution
Correct Answer
(D) \(x^2+x+1=0\)
Step-by-step Solution
Detailed explanation
Hints : Roots are \(\omega, \omega^2\) Let \(\alpha=\omega, \beta=\omega^2\) \(\alpha^{19}=\omega, \beta^7=\omega^2\) \(\therefore\) Equation remains same i.e. \(\mathrm{x}^2+\mathrm{x}+1=0\)
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