Complex quadratic polynomial information

A complex quadratic polynomial is a quadratic polynomial whose coefficients and variable are complex numbers. Quadratic polynomials have the following...

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...

particular, it is a second-degree polynomial equation, since the greatest power is two. A quadratic equation with real or complex coefficients has two solutions...

square. Quadratic function (or quadratic polynomial), a polynomial function that contains terms of at most second degree Complex quadratic polynomials, are...

number theory, and algebraic geometry. The discriminant of the quadratic polynomial a x 2 + b x + c {\displaystyle ax^{2}+bx+c} is b 2 − 4 a c , {\displaystyle...

algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation. Other ways of solving quadratic equations,...

elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form a x 2 + b x + c {\displaystyle ax^{2}+bx+c} to the form...

polynomials, quadratic polynomials and cubic polynomials. For higher degrees, the specific names are not commonly used, although quartic polynomial (for...

an algebraic equation or polynomial equation is an equation of the form P = 0 {\displaystyle P=0} , where P is a polynomial with coefficients in some...

In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, 4 x 2...

pairs which when multiplied give quadratic polynomials with real coefficients. Since every polynomial with complex coefficients can be factored into...

image and video show the attractor of a second order 3-D Sprott-type polynomial, originally computed by Nicholas Desprez using the Chaoscope freeware...

of some complex quadratic maps. A map is a formula for computing a value of a variable based on its own previous value or values; a quadratic map is one...

finite rational maps). A complex quadratic polynomial has only one critical point. By a suitable conjugation any quadratic polynomial can be transformed into...

Best-fit curves may vary from simple linear equations to more complex quadratic, polynomial, exponential, and periodic curves. Curve fitting Data and information...

integer or natural number variable). Examples of quadratic growth include: Any quadratic polynomial. Certain integer sequences such as the triangular...

univariate polynomial is either one or two. More precisely, the irreducible polynomials are the polynomials of degree one and the quadratic polynomials a x 2...

numbers. If the quadratic polynomial is monic (a = 1), the roots are further qualified as quadratic integers. Gaussian integers, complex numbers a + bi...

mathematics, a Hurwitz polynomial, named after Adolf Hurwitz, is a polynomial whose roots (zeros) are located in the left half-plane of the complex plane or on the...

biquadratic function refers to a quadratic function of a square (or, equivalently, to the function defined by a quartic polynomial without terms of odd degree)...

In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is a x 2 + b x + c = 0 , {\displaystyle ax^{2}+bx+c=0...

factorization with linear or quadratic real factors. For computing these real or complex factorizations, one needs the roots of the polynomial, which may not be...

has a major use in the formula for roots of a quadratic equation; quadratic fields and rings of quadratic integers, which are based on square roots, are...

of a Taylor series is a polynomial of degree n that is called the nth Taylor polynomial of the function. Taylor polynomials are approximations of a function...

their minimal polynomials have degree four. Here and in the following, the quadratic integers that are considered belong to a quadratic field Q ( D )...

of algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more...

bifurcation values again: In the case of the Mandelbrot set for complex quadratic polynomial f ( z ) = z 2 + c {\displaystyle f(z)=z^{2}+c} the Feigenbaum...

roots – it is zero if and only if the polynomial has a multiple root, and for quadratic and cubic polynomials it is positive if and only if all roots...