Question

If α, β and γ are the roots of x³ + 8 = 0, then the equation
whose roots are α², β² and γ² is
(a) x³ - 8 = 0 (b) x³ - 16 = 0 (c) x³ + 64 = 0 (d) x³ - 64 = 0

Answer 1

Answer:

(d)

Step-by-step explanation:

If we use identity of 3rd degree polynomial here,

we have (x+2)(x²-2x+4)=0.

Root of x+2=0 is -2.

Let γ=-2. Therefore, γ²=4.

We use relation on quadratic equation on x²-2x+4=0.

Let the roots be α, β. We have α+β=2, α×β=4.

Therefore, α²+β²=-4, (αβ)²=16.

The quadratic equation will be x²-(α²+β²)x+(αβ)²=0.

Therefore, x²+4x+16=0.

Now, we multiply them all. We will get (x-4)(x²+4x+16)=0.

Therefore, the equation is x³-64=0. Or (d).