Question

Solve 2x³+4x² - 16x=0.
The roots are x =
X =
and x =

Answer 1

x ∈ {-4, 0, 2}

Explanation:

You want the solutions to the cubic 2x³ +4x² -16x = 0.

Factors

We observe that x and 2 are factors of all terms, so this can be written ...

2x(x² +2x -8) = 0

The quadratic will have binomial factors with constants that are factors of -8 that have a sum of 2.

2x(x +4)(x -2) = 0

Solutions

Solutions are the values of x that make the factors zero:

x = 0

x +4 = 0 ⇒ x = -4

x -2 = 0 ⇒ x = 2

The solutions are x = -4, 0, 2.