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Question: Answered & Verified by Expert
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
MathematicsQuadratic EquationWBJEEWBJEE 2010
Options:
  • 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 $x^2+x+1=0$
Solution:
2585 Upvotes Verified Answer
The correct answer is: $x^2+x+1=0$
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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