Polynomial function theorems for zeros

Polynomial function theorems for zeros are a set of theorems aiming to find (or determine the nature) of the complex zeros of a polynomial function of the form $p(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+...+a_{2}x^{2}+a_{1}x+a_{0}$ where $a_{i}(i=0,1,2,...,n)$ are real and $a_{n}\neq 0$.

Found in most precalculus textbooks, these theorems include:

• The fundamental theorem of algebra,
• Descartes' rules of signs,
• Conjugate pairs theorem,
• Bounds of zeros theorem,
• Remainder theorem,
• Rational zeros theorem, and
• Imtermediate value theorem