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  2. 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 ...

  3. Quadratic formula - Wikipedia

    en.wikipedia.org/wiki/Quadratic_formula

    A similar but more complicated method works for cubic equations, which have three resolvents and a quadratic equation (the "resolving polynomial") relating ⁠ ⁠ and ⁠ ⁠, which one can solve by the quadratic equation, and similarly for a quartic equation (degree 4), whose resolving polynomial is a cubic, which can in turn be solved. [14]

  4. Quadratic equation - Wikipedia

    en.wikipedia.org/wiki/Quadratic_equation

    [4] [5] Because the quadratic equation involves only one unknown, it is called "univariate". The quadratic equation contains only powers of x that are non-negative integers, and therefore it is a polynomial equation. In particular, it is a second-degree polynomial equation, since the greatest power is two.

  5. Elementary algebra - Wikipedia

    en.wikipedia.org/wiki/Elementary_algebra

    In general, a quadratic equation can be expressed in the form + + =, [42] where a is not zero (if it were zero, then the equation would not be quadratic but linear). Because of this a quadratic equation must contain the term a x 2 {\displaystyle ax^{2}} , which is known as the quadratic term.

  6. 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 ...

  7. List of equations - Wikipedia

    en.wikipedia.org/wiki/List_of_equations

    2.1 Mathematics. 2.2 Physics. ... Download as PDF; Printable version; In other projects ... Polynomial equation. Linear equation; Quadratic equation;

  8. Vieta jumping - Wikipedia

    en.wikipedia.org/wiki/Vieta_jumping

    We know that one root of this equation is x 1 = A. By standard properties of quadratic equations, we know that the other root satisfies x 2 = kB – A and x 2 = ⁠ B 2 – k / A ⁠. The first expression for x 2 shows that x 2 is an integer, while the second expression implies that x 2 ≠ 0 since k is not a perfect square.

  9. Additional Mathematics - Wikipedia

    en.wikipedia.org/wiki/Additional_Mathematics

    Additional Mathematics is a qualification in mathematics, commonly taken by students in high-school (or GCSE exam takers in the United Kingdom). It features a range of problems set out in a different format and wider content to the standard Mathematics at the same level.

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