The fundamental theorem of algebra says that every polynomial of degree n > 1 has exactly n roots, including multiple and complex roots. This means that a linear equation will have one root, a quadratic equation will have two, and a cubic equation will have three.
When you solve a polynomial with complex coefficients, you can always use the fundamental theorem of algebra to find the roots of the polynomial. This is called d'Alembert's theorem or the d'Alembert-Gauss theorem, and it includes both real and imaginary polynomials with complex coefficients.
If you want to prove the fundamental theorem, then you need to count all of the possible roots that can be found in a polynomial. This is a difficult thing to do, but it's important.
What do you think is the easiest way to find all of the possible roots that can be found?
A good way to do this is by factorising the polynomial. Then you can count all of the different ways that a factor can change the polynomial.
For example, you can factor f(x) into x2 and x1.
You can also find all of the possible roots that can be obtained by using Descartes' rule of signs. These numbers can then be used to determine the possible number of zeros that a polynomial has.