- Root (mathematics)
:"This article is about the zeros of a function, which should not be confused with the value at zero. You may also want information on the

Nth root s of numbers instead."In

mathematics , a**root**(or a**zero**) of a complex-valued function $f$ is a member $x$ of the domain of $f$ such that $f(x)$**vanishes**at $x$, that is,:$x\; ext\{\; such\; that\; \}\; f(x)\; =\; 0,.$

In other words, a "root" of a function $f$ is a value for $x$ that produces a result of zero ("0"). For example, consider the function $f$ defined by the following formula::$f(x)=x^2-6x+9\; ,.$This function has a root at 3 because $f(3)\; =\; 3^2\; -\; 6(3)\; +\; 9\; =\; 0$.

If the function is mapping from

real number s to real numbers, its zeros are the points where its graph meets the "x"-axis. The x-value of such a point is called x-intercept. Therefore in this situation a root can be called an**"x"-intercept**.The word

**root**can also refer to thenth root of a number,**a**, as in $a^\{1/n\}\; =\; sqrt\; [n]\; \{a\}$.Thesquare root of a number,**a**, is $a^\{1/2\}\; =\; sqrt\; [2]\; \{a\}\; =\; sqrt\{a\}$.A substantial amount of mathematics was developed in order to find roots of various functions, especially

polynomial s. One wide-ranging concept,complex number s, was developed to handle the roots of quadratic orcubic equation s with negativediscriminant (that is, those leading to expressions involving the square root of negative numbers).All real polynomials of odd degree have a real number as a root. Many real polynomials of even degree do not have a real root, but the

fundamental theorem of algebra states that every polynomial of degree $n$ has $n$ complex roots, counted with their multiplicities. The non-real roots of polynomials with real coefficients come in conjugate pairs.Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots.One of the most important

unsolved problems in mathematics concerns the location of the roots of theRiemann zeta function .**ee also***

zero (complex analysis)

*pole (complex analysis)

* other roots

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2010.*

### Look at other dictionaries:

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