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For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated scientific problems; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; and they are used in calculus and ...
A trigonometric equation is an equation g = 0 where g is a trigonometric polynomial. Such an equation may be converted into a polynomial system by expanding the sines and cosines in it (using sum and difference formulas), replacing sin(x) and cos(x) by two new variables s and c and adding the new equation s 2 + c 2 – 1 = 0.
In mathematics, an algebraic equation or polynomial equation is an equation of the form =, where P is a polynomial with coefficients in some field, often the field of the rational numbers. For example, x 5 − 3 x + 1 = 0 {\displaystyle x^{5}-3x+1=0} is an algebraic equation with integer coefficients and
An algebraic equation or polynomial equation is an equation in which both sides are polynomials (see also system of polynomial equations). These are further classified by degree: linear equation for degree one; quadratic equation for degree two; cubic equation for degree three; quartic equation for degree four; quintic equation for degree five
Polynomial equations of degree up to four can be solved exactly using algebraic methods, of which the quadratic formula is the simplest example. Polynomial equations with a degree of five or higher require in general numerical methods (see below) or special functions such as Bring radicals, although some specific cases may be solvable ...
This is the case of the equation = for any n, and the equations defined by cyclotomic polynomials, all of whose solutions can be expressed in radicals. Abel's proof of the theorem does not explicitly contain the assertion that there are specific equations that cannot be solved by radicals.
The quadratic equation contains only powers of x that are non-negative integers, and therefore it is a polynomial equation. ... As an example, x 2 + 5x + 6 factors as ...
Finding the roots (zeros) of a given polynomial has been a prominent mathematical problem.. Solving linear, quadratic, cubic and quartic equations in terms of radicals and elementary arithmetic operations on the coefficients can always be done, no matter whether the roots are rational or irrational, real or complex; there are formulas that yield the required solutions.