Wouldn’t it be nice to be able to find out exactly where a function crosses the x-axis?
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
In other words, find all the Zeros of a Polynomial Function!
Thanks to the Rational Zeros Test we can!
In fact, we are going to see that combining our knowledge of the Factor Theorem and the Remainder Theorem, along with our powerful new skill of identifying p and q, we are going to be able to find all the zeros (roots) of any polynomial function.
Zero Factor Theorem
Remember the Fundamental Theorem of Algebra which states that whatever the degree of the polynomial, that is exactly the number of zeros (roots or x-intercepts) we will get, as Paul’s Online Notes so accurately states.
This will definitely aid us in our quest to finding all the zeros.
Yes, this does imply that sometimes polynomials will have zeros consisting of real numbers, and other times the roots will be imaginary or complex.
But don’t worry, they are easy to work with and not hard to find.
This lesson we’re going to learn how to find all types of roots, in one easy to follow method by walking through countless examples in detail.
Finding Zeros – Video
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