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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

    Figure 1. Plots of quadratic function y = ax 2 + bx + c, varying each coefficient separately while the other coefficients are fixed (at values a = 1, b = 0, c = 0). A quadratic equation whose coefficients are real numbers can have either zero, one, or two distinct real-valued solutions, also called roots.

  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. Algebraic number - Wikipedia

    en.wikipedia.org/wiki/Algebraic_number

    The square root of 2 is an algebraic number equal to the length of the hypotenuse of a right triangle with legs of length 1.. An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients.

  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. Cubic equation - Wikipedia

    en.wikipedia.org/wiki/Cubic_equation

    If <, the cubic has one real root and two non-real complex conjugate roots. This can be proved as follows. First, if r is a root of a polynomial with real coefficients, then its complex conjugate is also a root. So the non-real roots, if any, occur as pairs of complex conjugate roots.

  9. Quadratic function - Wikipedia

    en.wikipedia.org/wiki/Quadratic_function

    The graph of a real single-variable quadratic function is a parabola. If a quadratic function is equated with zero, then the result is a quadratic equation. The solutions of a quadratic equation are the zeros (or roots) of the corresponding quadratic function, of which there

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