A polynomial with the leading coefficient 1 is called a  Complex Conjugate Rootcubicdegree 0discriminantequalFundamentalmonic polynomialno real rootsnon-negativequadraticquarticradical solutionreal and distinctsimple rootzero polynomial.

Every nonzero constant is a polynomial of  Complex Conjugate Rootcubicdegree 0discriminantequalFundamentalmonic polynomialno real rootsnon-negativequadraticquarticradical solutionreal and distinctsimple rootzero polynomial .

The constant 0 is also a polynomial called the  Complex Conjugate Rootcubicdegree 0discriminantequalFundamentalmonic polynomialno real rootsnon-negativequadraticquarticradical solutionreal and distinctsimple rootzero polynomial; its degree is not defined.

The degree of a polynomial is a  Complex Conjugate Rootcubicdegree 0discriminantequalFundamentalmonic polynomialno real rootsnon-negativequadraticquarticradical solutionreal and distinctsimple rootzero polynomial integer.

The  Complex Conjugate Rootcubicdegree 0discriminantequalFundamentalmonic polynomialno real rootsnon-negativequadraticquarticradical solutionreal and distinctsimple rootzero polynomial is the only polynomial with leading coefficient 0 .

Polynomials of degree two are called  Complex Conjugate Rootcubicdegree 0discriminantequalFundamentalmonic polynomialno real rootsnon-negativequadraticquarticradical solutionreal and distinctsimple rootzero polynomial polynomials.

Polynomials of degree three are called  Complex Conjugate Rootcubicdegree 0discriminantequalFundamentalmonic polynomialno real rootsnon-negativequadraticquarticradical solutionreal and distinctsimple rootzero polynomial polynomials.

Polynomial of degree four are called  Complex Conjugate Rootcubicdegree 0discriminantequalFundamentalmonic polynomialno real rootsnon-negativequadraticquarticradical solutionreal and distinctsimple rootzero polynomial polynomials.

For the quadratic equation ax²+bx+c=0,b²−4ac is called the  Complex Conjugate Rootcubicdegree 0discriminantequalFundamentalmonic polynomialno real rootsnon-negativequadraticquarticradical solutionreal and distinctsimple rootzero polynomial.

∆ = 0 if, and only if, the roots are  Complex Conjugate Rootcubicdegree 0discriminantequalFundamentalmonic polynomialno real rootsnon-negativequadraticquarticradical solutionreal and distinctsimple rootzero polynomial.

∆ > 0 if, and only if, the roots are  Complex Conjugate Rootcubicdegree 0discriminantequalFundamentalmonic polynomialno real rootsnon-negativequadraticquarticradical solutionreal and distinctsimple rootzero polynomial.

∆ < 0 if, and only if, the quadratic equation has  Complex Conjugate Rootcubicdegree 0discriminantequalFundamentalmonic polynomialno real rootsnon-negativequadraticquarticradical solutionreal and distinctsimple rootzero polynomial.

If a is a root of multiplicity 1 for a polynomial equation, then a is called a  Complex Conjugate Rootcubicdegree 0discriminantequalFundamentalmonic polynomialno real rootsnon-negativequadraticquarticradical solutionreal and distinctsimple rootzero polynomial of the polynomial equation.

A solution of a polynomial equation written only using its coefficients, the four basic arithmetic operators ,and rational exponentiation is called a  Complex Conjugate Rootcubicdegree 0discriminantequalFundamentalmonic polynomialno real rootsnon-negativequadraticquarticradical solutionreal and distinctsimple rootzero polynomial.

The  Complex Conjugate Rootcubicdegree 0discriminantequalFundamentalmonic polynomialno real rootsnon-negativequadraticquarticradical solutionreal and distinctsimple rootzero polynomial Theorem of Algebra : A polynomial of degree n ≥1 has at least one root in C.

 Complex Conjugate Rootcubicdegree 0discriminantequalFundamentalmonic polynomialno real rootsnon-negativequadraticquarticradical solutionreal and distinctsimple rootzero polynomial Theorem : Imaginary (nonreal complex) roots occur as conjugate pairs, if the coefficients of the polynomial are real.