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  2. Quadratic equation - Wikipedia

    en.wikipedia.org/wiki/Quadratic_equation

    Completing the square can be used to derive a general formula for solving quadratic equations, called the quadratic formula. [9] The mathematical proof will now be briefly summarized. [ 10 ] It can easily be seen, by polynomial expansion , that the following equation is equivalent to the quadratic equation: ( x + b 2 a ) 2 = b 2 − 4 a c 4 a 2 ...

  3. Muller's method - Wikipedia

    en.wikipedia.org/wiki/Muller's_method

    Muller's method is a root-finding algorithm, a numerical method for solving equations of the form f(x) = 0. It was first presented by David E. Muller in 1956. Muller's method proceeds according to a third-order recurrence relation similar to the second-order recurrence relation of the secant method .

  4. Quadratic formula - Wikipedia

    en.wikipedia.org/wiki/Quadratic_formula

    Any generic method or algorithm for solving quadratic equations can be applied to an equation with symbolic coefficients and used to derive some closed-form expression equivalent to the quadratic formula. Alternative methods are sometimes simpler than completing the square, and may offer interesting insight into other areas of mathematics.

  5. Inverse quadratic interpolation - Wikipedia

    en.wikipedia.org/wiki/Inverse_quadratic...

    In numerical analysis, inverse quadratic interpolation is a root-finding algorithm, meaning that it is an algorithm for solving equations of the form f(x) = 0. The idea is to use quadratic interpolation to approximate the inverse of f. This algorithm is rarely used on its own, but it is important because it forms part of the popular Brent's method.

  6. Solving quadratic equations with continued fractions - Wikipedia

    en.wikipedia.org/wiki/Solving_quadratic...

    The quadratic equation on a number can be solved using the well-known quadratic formula, which can be derived by completing the square. That formula always gives the roots of the quadratic equation, but the solutions are expressed in a form that often involves a quadratic irrational number, which is an algebraic fraction that can be evaluated ...

  7. Completing the square - Wikipedia

    en.wikipedia.org/wiki/Completing_the_square

    In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form ⁠ + + ⁠ to the form ⁠ + ⁠ for some values of ⁠ ⁠ and ⁠ ⁠. [1] In terms of a new quantity ⁠ x − h {\displaystyle x-h} ⁠ , this expression is a quadratic polynomial with no linear term.

  8. Polynomial interpolation - Wikipedia

    en.wikipedia.org/wiki/Polynomial_interpolation

    The original use of interpolation polynomials was to approximate values of important transcendental functions such as natural logarithm and trigonometric functions.Starting with a few accurately computed data points, the corresponding interpolation polynomial will approximate the function at an arbitrary nearby point.

  9. Cubic function - Wikipedia

    en.wikipedia.org/wiki/Cubic_function

    The solutions of this equation are the x-values of the critical points and are given, using the quadratic formula, by =. The sign of the expression Δ 0 = b 2 – 3ac inside the square root determines the number of critical points. If it is positive, then there are two critical points, one is a local maximum, and the other is a local minimum.