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  2. Quadratic equation - Wikipedia

    en.wikipedia.org/wiki/Quadratic_equation

    Quadratic equation. In mathematics, a quadratic equation (from Latin quadratus ' square ') is an equation that can be rearranged in standard form as [1] where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.)

  3. Equation solving - Wikipedia

    en.wikipedia.org/wiki/Equation_solving

    Equation solving. The quadratic formula, the symbolic solution of the quadratic equation ax2 + bx + c = 0. An example of using Newton–Raphson method to solve numerically the equation f(x) = 0. In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated ...

  4. Quadratic formula - Wikipedia

    en.wikipedia.org/wiki/Quadratic_formula

    Quadratic formula. The roots of the quadratic function y = ⁠ 1 2 ⁠x2 − 3x + ⁠ 5 2 ⁠ are the places where the graph intersects the x -axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.

  5. Solving quadratic equations with continued fractions - Wikipedia

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

    Solving quadratic equations with continued fractions. In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is. where a ≠ 0. 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 ...

  6. Extraneous and missing solutions - Wikipedia

    en.wikipedia.org/wiki/Extraneous_and_missing...

    Extraneous and missing solutions. In mathematics, an extraneous solution (or spurious solution) is one which emerges from the process of solving a problem but is not a valid solution to it. [1] A missing solution is a valid one which is lost during the solution process. Both situations frequently result from performing operations that are not ...

  7. System of polynomial equations - Wikipedia

    en.wikipedia.org/wiki/System_of_polynomial_equations

    A system of polynomial equations (sometimes simply a polynomial system) is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in several variables, say x1, ..., xn, over some field k. A solution of a polynomial system is a set of values for the xi s which belong to some algebraically closed field extension K of k ...