Chapter 4.1, Problem 28E

To determine

whether 3 is a root of $a^4-13a^2+12a=0$ .

Answer to Problem 28E

Yes

Explanation of Solution

Given information: $a^4-13a^2+12a=0$

Calculation:

To determine if 3 is a root of this equation, plug it in.

If we find that $a=3$ does satisfy $a^4-13a^2+12a=0,$

Then $a=3$ is a root

  $a^4-13a^2+12a=0$

  $\begin{array}{l}{\left(3\right)}^4-13{\left(3\right)}^2+12\left(3\right)=0\\ 81-117+36=0\\ 0=0\\ \to \text{Yes}\end{array}$