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Consider the function ''f'' defined by the following formula:
:f(x)=x^2-6x+9 \,
The "root" of a function (f) is the value for ''x'' that produces a result of zero(0). For the above function, 3 is the root of ''f'', because ''f''(3) = 32 - 6(3) + 9 = 0.

If the function is mapping from Real Number s to Real Number s, its zeros are essentially where its graph hits the X-axis . In this situation, the root can be called a ''x''-intercept. Although, not all graphs cross the x-axis and in these cases the root is a Complex Number , where it is a multiple of the root of negative one -1 . Complex roots may only occur in pairs and indeed linear graphs never have complex roots.

The word root can also refer to a number in the form ''x''1/''a'', such as the Square Root or Other Roots .

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 Equation s with negative Discriminant (that is, those leading to expressions involving the square root of Negative Numbers ).

All Real Polynomial s 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 real polynomials come in conjugate pairs.

One of the most important unsolved problems in mathematics concerns the location of the roots of the Riemann Zeta Function .


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