I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.
Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.
Paul
February 18, 2026
Section 1.1 : Review : Functions
14. Determine all the roots of \(W\left( x \right) = {x^4} + 6{x^2} - 27\).
Show SolutionSet the function equal to zero and factor the left side as much as possible.
\[{x^4} + 6{x^2} - 27 = \left( {{x^2} - 3} \right)\left( {{x^2} + 9} \right) = 0\]Don’t so locked into quadratic equations that the minute you see an equation that is not quadratic you decide you can’t deal with it. While this function was not a quadratic it still factored in an obvious manner.
Now, the second term will never be zero (for any real value of \(x\) anyway and in this class those tend to be the only ones we are interested in) and so we can ignore that term. The first will be zero if,
\[{x^2} - 3 = 0\hspace{0.25in} \Rightarrow \hspace{0.25in}{x^2} = 3\hspace{0.25in}\hspace{0.25in} \Rightarrow \hspace{0.25in}x = \pm \sqrt 3 \]So, we have two real roots of this function. Note that if we allowed complex roots (which again, we aren’t really interested in for this course) there would also be two complex roots from the second term as well.