Question

If α and β are the roots of the equation x² + x + 1 = 0, then the equation whose roots are α¹⁹ and β⁷ is 

• (A) x² – x – 1 = 0
• (B) x² – x + 1 = 0
• (C) x² + x – 1= 0
• (D) x² + x + 1 = 0

Answer 1

The Correct Option is D

Explanation:
$\alpha$ and $\beta$ are the roots of $x^2+x+1=0$ $\alpha =\omega \beta ={\omega }^2$${\alpha }^{19}=\omega {\beta }^7={\omega }^2$$x^2-({\alpha }^{19}+{\beta }^{\prime })x+{\alpha }^{19}{\beta }^7=0$Thou,$x^2-(\omega +{\omega }^2)x+\omega \cdot {\omega }^2=0$$x^2+x+1=0$