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, *x*2 − 4*x* + 7 is a quadratic polynomial, while *x***3** − 4*x* + 7 is not.

Read more about Quadratic Polynomial: Coefficients, Degree, Variables

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**quadratic**formula expressed the roots of a**quadratic polynomial**as a rational function in terms of the square root of the discriminant, the roots of a**quadratic polynomial**are in the same field as ... 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 only if it is positive (not ... Further, for a**quadratic polynomial**with rational coefficients, it factors over the rationals if and only if the discriminant – which is necessarily a rational number, being a**polynomial**in the ...**Quadratic Polynomial**- Variables - N Variables Case

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**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 ... 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 ...