Question

3. What are the roots of the polynomial y = x³ - 8?

Answer 1

Explanation:

x^3 is a perfect cube, 8 is a perfect cube, so we use difference of cubes.

`{a}^(3) - {b}^(3) = (a - b)( {a}^(2) + ab + {b}^(2) )`

Cube root of x^3 is x.

Cube root of 8 is 2

So

a=x

b= 2.

`(x - 2)( {x}^(2) - 2x + 4)`

Set these equations equal to zero

`x - 2 = 0`

`x = 2`

`{x}^(2) - 2x + 4 = 0`

If we do the discriminant, we get a negative answer so we would have two imaginary solutions,

Thus the only real root is 2.

If you want imaginary solutions, apply the quadratic formula.

`1 + i √( 3 )`

and

`1 - i √(3)`