Q43. - Algebra 2

Question

Solve each equation.

 

$x^4-5x^2+4=0$

Step-by-Step Solution

Answer

The solutions are -2, -1, 1 and 2.

Step 1. Given Information.

Given, to solve the equation $x^4-5x^2+4=0$.

Step 2. Calculation .

Solving the equation:

 

 $\begin{array}{l}{\left(x^2\right)}^2-5\left(x^2\right)+4=0\\ {\left(x^2\right)}^2-\left(x^2\right)-4\left(x^2\right)+4=0\left(\text{Writing it in the quadratic form}\right)\\ \left(x^2\right)\left(x^2-1\right)-4\left(x^2-1\right)=0\\ \left(x^2-1\right)\left(x^2-4\right)=0\left(\text{Factoring the trinomial}\right)\\ \left(x^2-1^2\right)\left(x^2-2^2\right)=0\\ \left(x-1\right)\left(x+1\right)\left(x-2\right)\left(x+2\right)=0\left(\text{Factoring each difference of squares}\right)\end{array}$
 

Using the Zero Product Property:

 

 $\begin{array}{l}x-1=0\text{ or }x+1=0\text{ or }x-2=0\text{ or }x+2=0\\ x=1\text{ or }x=-1\text{ or }x=2\text{ or }x=-2\end{array}$

Step 3. Conclusion .

Hence, the solutions are -2, -1, 1 and 2.