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  2. Vieta's formulas - Wikipedia

    en.wikipedia.org/wiki/Vieta's_formulas

    Vieta's formulas are frequently used with polynomials with coefficients in any integral domain R.Then, the quotients / belong to the field of fractions of R (and possibly are in R itself if happens to be invertible in R) and the roots are taken in an algebraically closed extension.

  3. Sum of radicals - Wikipedia

    en.wikipedia.org/wiki/Sum_of_radicals

    In mathematics, a sum of radicals is defined as a finite linear combination of n th roots: =, where , are natural numbers and , are real numbers.. A particular special case arising in computational complexity theory is the square-root sum problem, asking whether it is possible to determine the sign of a sum of square roots, with integer coefficients, in polynomial time.

  4. Newton's identities - Wikipedia

    en.wikipedia.org/wiki/Newton's_identities

    Denoting by h k the complete homogeneous symmetric polynomial (that is, the sum of all monomials of degree k), the power sum polynomials also satisfy identities similar to Newton's identities, but not involving any minus signs.

  5. Square-root sum problem - Wikipedia

    en.wikipedia.org/wiki/Square-root_sum_problem

    SRS can be solved in polynomial time in the Real RAM model. [3] However, its run-time complexity in the Turing machine model is open, as of 1997. [1] The main difficulty is that, in order to solve the problem, the square-roots should be computed to a high accuracy, which may require a large number of bits.

  6. Arithmetic - Wikipedia

    en.wikipedia.org/wiki/Arithmetic

    Roots are a special type of exponentiation using a fractional exponent. For example, the square root of a number is the same as raising the number to the power of 1 2 {\displaystyle {\tfrac {1}{2}}} and the cube root of a number is the same as raising the number to the power of 1 3 {\displaystyle {\tfrac {1}{3}}} .

  7. Geometrical properties of polynomial roots - Wikipedia

    en.wikipedia.org/wiki/Geometrical_properties_of...

    The complex conjugate root theorem states that if the coefficients of a polynomial are real, then the non-real roots appear in pairs of the form (a + ib, a – ib).. It follows that the roots of a polynomial with real coefficients are mirror-symmetric with respect to the real axis.

  8. Nested radical - Wikipedia

    en.wikipedia.org/wiki/Nested_radical

    In the case of two nested square roots, the following theorem completely solves the problem of denesting. [2]If a and c are rational numbers and c is not the square of a rational number, there are two rational numbers x and y such that + = if and only if is the square of a rational number d.

  9. Quintic function - Wikipedia

    en.wikipedia.org/wiki/Quintic_function

    Even for the first root that involves at most two square roots, the expression of the solutions in terms of radicals is usually highly complicated. However, when no square root is needed, the form of the first solution may be rather simple, as for the equation x 5 − 5 x 4 + 30 x 3 − 50 x 2 + 55 x − 21 = 0 , for which the only real solution is