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  2. Zero of a function - Wikipedia

    en.wikipedia.org/wiki/Zero_of_a_function

    In mathematics, a zero (also sometimes called a root) of a real-, complex-, or generally vector-valued function, is a member of the domain of such that () vanishes at ; that is, the function attains the value of 0 at , or equivalently, is a solution to the equation () =. [1]

  3. Quadratic equation - Wikipedia

    en.wikipedia.org/wiki/Quadratic_equation

    When there is only one distinct root, it can be interpreted as two roots with the same value, called a double root. When there are no real roots, the coefficients can be considered as complex numbers with zero imaginary part , and the quadratic equation still has two complex-valued roots, complex conjugates of each-other with a non-zero ...

  4. Quadratic formula - Wikipedia

    en.wikipedia.org/wiki/Quadratic_formula

    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 equation, called the roots or zeros, can be found using the quadratic formula,

  5. nth root - Wikipedia

    en.wikipedia.org/wiki/Nth_root

    By convention the principal value of this function, called the principal root and denoted ⁠ ⁠, is taken to be the n th root with the greatest real part and in the special case when x is a negative real number, the one with a positive imaginary part. The principal root of a positive real number is thus also a positive real number.

  6. Cubic equation - Wikipedia

    en.wikipedia.org/wiki/Cubic_equation

    The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the coefficients a, b, c, and d of the cubic equation are real numbers, then it has at least one real root (this is true for all odd-degree polynomial functions). All of the roots of the cubic equation can be found by ...

  7. Square root - Wikipedia

    en.wikipedia.org/wiki/Square_root

    The square root of a positive integer is the product of the roots of its prime factors, because the square root of a product is the product of the square roots of the factors. Since p 2 k = p k , {\textstyle {\sqrt {p^{2k}}}=p^{k},} only roots of those primes having an odd power in the factorization are necessary.

  8. Algebraic number - Wikipedia

    en.wikipedia.org/wiki/Algebraic_number

    An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio , ( 1 + 5 ) / 2 {\displaystyle (1+{\sqrt {5}})/2} , is an algebraic number, because it is a root of the polynomial x 2 − x − 1 .

  9. Quadratic function - Wikipedia

    en.wikipedia.org/wiki/Quadratic_function

    To convert the standard form to factored form, one needs only the quadratic formula to determine the two roots r 1 and r 2. To convert the standard form to vertex form, one needs a process called completing the square. To convert the factored form (or vertex form) to standard form, one needs to multiply, expand and/or distribute the factors.