Question

K(x) = x^3 +2x^2-x-2 find all roots

Answer 1

The all roots are equation are 1, - 1 and - 2.

Explanation:

The given cubic polynomial:

k(x) =
`x^3` + 2
`x^2` - x -2

To find, the all roots are
`x^3` + 2
`x^2` - x -2 = ?

∴ k(x) =
`x^3` + 2
`x^2` - x -2

⇒
`x^3` + 2
`x^2` - x -2 = 0

⇒
`x^2`(x + 2) - 1(x + 2) = 0

⇒ (
`x^2` - 1)(x + 2) = 0

⇒
`x^2` - 1 = 0 and x + 2 = 0

⇒
`x^2` - 1 = 0

⇒
`x^2` = 1

⇒ x = ± 1 = 1, - 1

or, x + 2 = 0

⇒ x = - 2

Thus, the all roots are equation are 1, - 1 and - 2.