root, in mathematics

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 x2+x−12=0, because (3)2+(3)−12=0 and (−4)2+(−4)−12=0. In the special case where f(x)=xna for some number a, a root of f is called an nth root of a, denoted by an or a1/n. For example, 2 is the third, or cube, root of 8 (83=2), since it satisfies the equation x3−8=0. Every number has n different (real or complex) nth 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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