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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
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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. $\mathrm{x}^2+\mathrm{x}+1=0$
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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