Question

Let $\alpha ,\beta$ be the roots of $x^2+x+1=0$. Then the equation whose roots are ${\alpha }^{229}$ and ${\alpha }^{1004}$ 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 1

Answer: (D)

$x^2+x+1=0$

$\alpha =\omega$

Hence,

${\alpha }^{229}=\omega$

${\alpha }^{1004}={\omega }^2$

Hence, the required equation is $x^2+x+1=0$