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  2. Solving quadratic equations with continued fractions

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

    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 as a decimal fraction only by applying an additional root extraction algorithm.

  3. Partial fraction decomposition - Wikipedia

    en.wikipedia.org/wiki/Partial_fraction_decomposition

    In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.

  4. Equating coefficients - Wikipedia

    en.wikipedia.org/wiki/Equating_coefficients

    In mathematics, the method of equating the coefficients is a way of solving a functional equation of two expressions such as polynomials for a number of unknown parameters. It relies on the fact that two expressions are identical precisely when corresponding coefficients are equal for each different type of term.

  5. Polynomial - Wikipedia

    en.wikipedia.org/wiki/Polynomial

    Nevertheless, formulas for solvable equations of degrees 5 and 6 have been published (see quintic function and sextic equation). When there is no algebraic expression for the roots, and when such an algebraic expression exists but is too complicated to be useful, the unique way of solving it is to compute numerical approximations of the ...

  6. 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]

  7. Extraneous and missing solutions - Wikipedia

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

    To begin solving, we multiply each side of the equation by the least common denominator of all the fractions contained in the equation. In this case, the least common denominator is () (+). After performing these operations, the fractions are eliminated, and the equation becomes: