Chapter 8.2, Problem 84SR

To determine

To solve: the equation and state the type of root.

Answer to Problem 84SR

The value of equation is $x=\pm \sqrt{3}i,\pm 3$ and the two roots are imaginary and two roots are real.

Explanation of Solution

Given information:

The equation is $x^4-81=0$ .

Calculation: to solve the equation, first factor and then simplify,

  $\begin{array}{l}{x}^4-81=0\\ \left(x-3\right)\left(x+3\right)\left(x^2+9\right)=0\text{ [factor]}\\ x=3,-3\\ x^2+9=0\\ x=\pm \sqrt{3}i\text{ [simplify]}\end{array}$

Thus, the roots of the equation is $x=\pm \sqrt{3}i,\pm 3$ and the two roots are imaginary and two root is real.