If α , β and γ are the roots of x 3 + 8 = 0 , then the equation whose roots are α 2 , β 2 a n d γ 2 is Options: A . &nbspx3−8=0 B . &nbspx3−16=0 C . &nbspx3+64=0 D . &nbspx3−64=0

Answer: Option D : D Let y = x 2 . then x = √ y ∴ x 3 + 8 = 0 ⇒ y 3 2 + 8 = 0 ⇒ y 3 = 64 ⇒ y 3 − 64 = 0 Thus the equation having roots α 2 , β 2 and γ 2 i s x 3 − 64 = 0

If α, β and γ are the roots of x3+8=0, then the equation

Question

α, β

and

γ

are the roots of

x^{3} + 8 = 0

, then the equation whose roots are

α^{2}, β^{2} a n d γ^{2}

Options:

A . x3−8=0

B . x3−16=0

C . x3+64=0

D . x3−64=0

Answer: Option D
:
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

α^{2}, β^{2}

and

γ^{2} i s x^{3} - 64 = 0

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