root

root, in mathematics, number or quantity r for which an equation f ( r ) = 0 holds true, where f is some function. If f is a polynomial, r is called a root of f; for example, r = 3 and r = - 4 are roots of the equation x ²+ x - 12 = 0, because (3)2+(3) - 12 = 0 and ( - 4)2+( - 4) - 12 = 0. In the special case where f ( x ) = x n - a for some number a, a root of f is called an n th root of a, denoted by n a or a 1/ n . For example, 2 is the third, or cube, root of 8 (38 = 2), since it satisfies the equation x 3 - 8 = 0. Every number has n different (real or complex) n th roots; e.g., there are two square roots of 9 (3 and - 3) since (3)(3) = 9 and ( - 3)( - 3) = 9.

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