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In mathematics, a root (or a zero) of a function f is an element x in the domain of f such that
- f(x) = 0.
For an important special case see zero (complex analysis).
Consider the equation:
- <math>f(x)=x^2-6x+9 \,<math>
Now 3 is called a root of f, because f(3) = 32 - (6 x 3) + 9 = 0.
If the function is mapping from real numbers to real numbers, its zeros are essentially where its graph hits the x-axis. In this situation, the root can be called a x-intercept.
A substantial amount of mathematics was developed in order to find roots of various functions, especially polynomials. The roots of a quadratic equation could be given by the study of the roots of polynomials of degree 3 led to the discovery of complex numbers.
Many real polynomials don't have a real number as a root, but the fundamental theorem of algebra states that every polynomial of degree (mathematics) n has n complex roots, counted with their multiplicities.
One of the most important unsolved problems in mathematics concerns the location of the zeros of the Riemann zeta function.
Compare with the concept of a pole.
The word root can also refer to a number in the form x1/a, such as the square root or other roots.
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