Question

What are the values of x in this equation?

x4 + 12x = 4x2 + 3x3
A. x = 0, x = -3, x = 2, and x = -2
B. x = 0 and x = 3
C. x = 0, x = 3, x = 2, and x = -2
D. x = 3, x = 2, and x = -2

Answer 1

A. x = 0, x = -3, x = 2, and x = -2

Explanation:

`x^(4) +12x=4x^(2) +3x^(3)`

by moving the terms on the left side to the right side

`x^(4) -3x^(3) -4x^(2) +12x = 0`

factor an
`x^(3)` from
`x^(4) -3x^(3)`

and factor - 4
`x` from
`-4x^(2) +12x`

the equation becomes :

`x^(3) (x - 3 )-4x (x - 3)` = 0

take
`(x - 3)` as a common factor the equation becomes :

`(x-3)(x^(3)-4x )` = 0

thus

`x - 3 = 0`⇒
`x = 3`

and

`x^(3) - 4x = 0` by factoring an x we get :

`x(x^(2)-4 ) =0` ⇒
`x` = 0 and
`x^(2) - 4 = 0`

`x^(2) - 4 =0`⇒
`x = 2` and
`x = -2`

Thus

the values are :

x = 0, x = -3, x = 2, and x = -2