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 ( 3 8 =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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