Fundamental theorem of algebra Video transcript Voiceover:So we have a polynomial right over here. On this page, regardless of how the topic is framed, the point will be to find all of the solutions to " polynomial equals zero ", even if the question is stated differently, such as "Find the roots of y equals polynomial ".
The x- intercepts of the graph are the same as the real-valued zeroes of the equation. This means that I won't have any complex-valued zeroes.
Specifically, an nth degree polynomial can have at most n real roots x-intercepts or zeros counting multiplicities. And I can narrow down my options further by "cheating" and looking at the graph: This is a fourth-degree polynomial, so it has, at most, four x-intercepts, and I can see all four of them on the graph.
The following graphs of polynomials exemplify each of the behaviors outlined in the above table. Let me write it this way. Intersections between spheres, cylinders, or other quadrics can be found using quartic equations.
Always check the list of possible zeroes as you go.
Remember that even if p x has even degree, it is not necessarily an even function. So I think you're starting to see a pattern.
This is what we wanted to prove.