Question

If α, β and γ are the roots of $x^3+8=0$, then the equation whose roots are ${\alpha }^2,{\beta }^{2}and{\gamma }^2$ is

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Let $y=x^2$. then $x=\sqrt{y}$

∴ $x^3+8=0$ ⇒ $y^{\frac{3}{2}}+8=0$

⇒ $y^3=64$ ⇒ $y^3-64=0$

Thus the equation having roots ${\alpha }^2,{\beta }^2$ and ${\gamma }^{2}is{x}^3-64=0$