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  2. Quadratic equation - Wikipedia

    en.wikipedia.org/wiki/Quadratic_equation

    Figure 1. Plots of quadratic function y = ax 2 + bx + c, varying each coefficient separately while the other coefficients are fixed (at values a = 1, b = 0, c = 0). A quadratic equation whose coefficients are real numbers can have either zero, one, or two distinct real-valued solutions, also called roots.

  3. Quadratic formula - Wikipedia

    en.wikipedia.org/wiki/Quadratic_formula

    Other ways of solving quadratic equations, such as completing the square, yield the same solutions. Given a general quadratic equation of the form ⁠ + + = ⁠, with ⁠ ⁠ representing an unknown, and coefficients ⁠ ⁠, ⁠ ⁠, and ⁠ ⁠ representing known real or complex numbers with ⁠ ⁠, the values of ⁠ ⁠ satisfying the ...

  4. Polynomial root-finding - Wikipedia

    en.wikipedia.org/wiki/Polynomial_root-finding

    Finding the root of a linear polynomial (degree one) is easy and needs only one division: the general equation + = has solution = /. For quadratic polynomials (degree two), the quadratic formula produces a solution, but its numerical evaluation may require some care for ensuring numerical stability.

  5. 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 ...

  6. Quadratic function - Wikipedia

    en.wikipedia.org/wiki/Quadratic_function

    If a quadratic function is equated with zero, then the result is a quadratic equation. The solutions of a quadratic equation are the zeros (or roots) of the corresponding quadratic function, of which there can be two, one, or zero. The solutions are described by the quadratic formula.

  7. Equation solving - Wikipedia

    en.wikipedia.org/wiki/Equation_solving

    Depending on the context, solving an equation may consist to find either any solution (finding a single solution is enough), all solutions, or a solution that satisfies further properties, such as belonging to a given interval. When the task is to find the solution that is the best under some criterion, this is an optimization problem. Solving ...

  8. Steffensen's method - Wikipedia

    en.wikipedia.org/wiki/Steffensen's_method

    The simplest form of the formula for Steffensen's method occurs when it is used to find a zero of a real function; that is, to find the real value that satisfies () =.Near the solution , the derivative of the function, ′, is supposed to approximately satisfy < ′ <; this condition ensures that is an adequate correction-function for , for finding its own solution, although it is not required ...

  9. Completing the square - Wikipedia

    en.wikipedia.org/wiki/Completing_the_square

    Given a quadratic polynomial of the form + the numbers h and k may be interpreted as the Cartesian coordinates of the vertex (or stationary point) of the parabola. That is, h is the x -coordinate of the axis of symmetry (i.e. the axis of symmetry has equation x = h ), and k is the minimum value (or maximum value, if a < 0) of the quadratic ...