Q57. - Algebra 2

Question

Solve the equation $x^5-5x^3+4x=0$.

Step-by-Step Solution

Answer

The solution for the equation is $x=0,-2,2,-1,1$.

Step 1. Write down the given equation.

The given equation is $x^5-5x^3+4x=0$.

Step 2. Simplify the equation.

The given equation $x^5-5x^3+4x=0$ is solved as:

$\begin{array}{c}{x}^5-5x^3+4x=0 ....\left(\text{Given}\right)\\ x\left(x^4-5x^2+4\right)=0\\ x=0 \text{or }{x}^4-5x^2+4=0\\ x=0 \text{or }\left(x^2-4\right)\left(x^2-1\right)=0\\ x=0 \text{or }{x}^2-4=0 \text{or }{x}^2-1=0\\ x=0 \text{or }x=\pm 2 \text{or }x=\pm 1\end{array}$

Step 3. Conclusion.

The solution for the given equation is $x=0,-2,2,-1,1$.