Solved: "Solve the polynomial equation. x3+121x=0"

High School
Algebra
Algebra I
Exponents and radicals

Khadija Wells

Answered question

2021-08-16

Solve the polynomial equation.
$x^{3} + 121 x = 0$

Answer & Explanation

jlo2niT

Skilled2021-08-17Added 96 answers

Since this is a degree three polynomial, it will have at most 3 solutions.
This means that once we find 3 solutions, we don't have to check for more.
First, factor the polynomial:
$x^{3} + 121 x = x (x^{2} + 121)$
from here, $x (x^{2} + 121) = 0$ when either x=0 or
$x^{2} + 121 = 0$ . Notice that x=0 gives us our first solution. So let’s consider the case when $x^{2} + 121 = 0$
We use algebra to solve for this:
$x^{2} + 121 = 0 \Rightarrow x^{2} = - 121 \Rightarrow x = \pm 11 i$
where $i = \sqrt{- 1} .$
If you are asked for real solutions then your answer is x=0. If you are allowed complex solutions, then you have three answers:
$x = 0, x = 11 i, x = - 11 i$

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Algebra I

Didn't find what you were looking for?