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In mathematics, a quadratic equation (from Latin quadratus ' square ') is an equation that can be rearranged in standard form as [1] where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0.
Quadratic formula. The roots of the quadratic function y = 1 2 x2 − 3x + 5 2 are the places where the graph intersects the x -axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula (in some countries referenced as Bhaskara's formula) is a closed-form expression describing ...
In mathematics, a quadratic polynomial is a polynomial of degree two in one or more variables. A quadratic function is the polynomial function defined by a quadratic polynomial. Before the 20th century, the distinction was unclear between a polynomial and its associated polynomial function; so "quadratic polynomial" and "quadratic function" were almost synonymous. This is still the case in ...
Quadratic forms are not to be confused with a quadratic equation, which has only one variable and includes terms of degree two or less. A quadratic form is one case of the more general concept of homogeneous polynomials .
In mathematics, the discriminant of a polynomial is a quantity that depends on the coefficients and allows deducing some properties of the roots without computing them. More precisely, it is a polynomial function of the coefficients of the original polynomial. The discriminant is widely used in polynomial factoring, number theory, and algebraic geometry . The discriminant of the quadratic ...
In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer. For a univariate polynomial, the degree of the polynomial is simply the ...
This quadratic equation has two solutions: and But if is substituted for in the original equation, the result is the invalid equation . This counterintuitive result occurs because in the case where , multiplying both sides by multiplies both sides by zero, and so necessarily produces a true equation just as in the first example.
Constant term. In mathematics, a constant term (sometimes referred to as a free term) is a term in an algebraic expression that does not contain any variables and therefore is constant. For example, in the quadratic polynomial , The number 3 is a constant term. [1]
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