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

quadratic function and quadratic polynomial are nearly synonymous and often abbreviated as quadratic. The graph of a real single-variable quadratic function...

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

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...

double root, or two complex solutions that are complex conjugates of each other. A quadratic equation always has two roots, if complex roots are included...

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...

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

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

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

algebra. Closed-form formulas for polynomial roots exist only when the degree of the polynomial is less than 5. The quadratic formula has been known since...

root of some monic polynomial (a polynomial whose leading coefficient is 1) of degree two whose coefficients are integers, i.e. quadratic integers are algebraic...

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...

Hurwitz polynomial (named after German mathematician Adolf Hurwitz) is a polynomial whose roots (zeros) are located in the left half-plane of the complex plane...

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)...

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

non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since...

Then, the other roots are the roots of this quadratic polynomial and can be found by using the quadratic formula. Cubics of the form t 3 + p t + q {\displaystyle...

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...

For instance, the square of the linear polynomial x + 1 is the quadratic polynomial (x + 1)2 = x2 + 2x + 1. One of the important properties of squaring...

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...

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

primitive third (cube) roots of unity, which are the roots of this quadratic polynomial, are − 1 + i 3 2 ,   − 1 − i 3 2 . {\displaystyle {\frac {-1+i{\sqrt...

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

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

method in higher dimensions is Broyden's method. If we use a polynomial fit to remove the quadratic part of the finite difference used in the secant method...

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...

popular complex dynamical system is given by the family of complex quadratic polynomials, a special case of rational maps. Such quadratic polynomials can...

in the spiral correspond to quadratic polynomials, and certain such polynomials, such as Euler's prime-generating polynomial x2 − x + 41, are believed to...

{\displaystyle N(z):=zz^{*}=x^{2}-y^{2},} an isotropic quadratic form. The collection D of all split-complex numbers z = x + y j {\displaystyle z=x+yj} for ⁠...

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