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The graph of a degree 1 polynomial (or linear function) f(x) = a0 + a1x, where a1 ≠ 0, is an oblique line with y-intercept a0 and slope a1 . The graph of a degree 2 polynomial. f(x) = a0 + a1x + a2x2, where a2 ≠ 0. is a parabola . The graph of a degree 3 polynomial. f(x) = a0 + a1x + a2x2 + a3x3, where a3 ≠ 0.
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 ...
Quadratic equation. 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. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.)
Rational root theorem. In algebra, the rational root theorem (or rational root test, rational zero theorem, rational zero test or p/q theorem) states a constraint on rational solutions of a polynomial equation with integer coefficients and . Solutions of the equation are also called roots or zeros of the polynomial on the left side.
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 ...
The first class is the discriminant of an algebraic number field, which, in some cases including quadratic fields, is the discriminant of a polynomial defining the field. Discriminants of the second class arise for problems depending on coefficients, when degenerate instances or singularities of the problem are characterized by the vanishing of ...
The factor theorem is also used to remove known zeros from a polynomial while leaving all unknown zeros intact, thus producing a lower degree polynomial whose zeros may be easier to find. Abstractly, the method is as follows: [ 3] Deduce the candidate of zero of the polynomial from its leading coefficient and constant term .
The cyclotomic polynomials are monic polynomials with integer coefficients that are irreducible over the field of the rational numbers. Except for n equal to 1 or 2, they are palindromes of even degree. The degree of , or in other words the number of n th primitive roots of unity, is , where is Euler's totient function .