In mathematics, a quadratic polynomial or quadratic is a polynomial of degree two, also called second-order polynomial. That means the exponents of the polynomial's variables are no larger than 2. For example, x2 − 4x + 7 is a quadratic polynomial, while x3 − 4x + 7 is not.

Quadratic Polynomial - Variables - N Variables Case
... In the general case, a quadratic polynomial in n variables x1.. ... xn can be written in the form where Q is a symmetric n-dimensional matrix, P is an n-dimensional vector, and R a constant ...
... A complex quadratic polynomial is a quadratic polynomial whose coefficients are complex numbers ...
Discriminant - Nature of The Roots - Quadratic
... Because the quadratic formula expressed the roots of a quadratic polynomial as a rational function in terms of the square root of the discriminant, the ... Thus in particular for a quadratic polynomial with real coefficients, a real number has real square roots if and only if it is nonnegative, and these roots are distinct if and ... Further, for a quadratic polynomial with rational coefficients, it factors over the rationals if and only if the discriminant – which is necessarily a ...
Quadratic Equation - Derivations of The Quadratic Formula - By Lagrange Resolvents
... An alternative way of deriving the quadratic formula is via the method of Lagrange resolvents, which is an early part of Galois theory ... This method can be generalized to give the roots of cubic polynomials and quartic polynomials, and leads to Galois theory, which allows one to understand the solution of ... Given a monic quadratic polynomial assume that it factors as Expanding yields where and Since the order of multiplication does not matter, one can switch α and β and the values of p and q will not ...