Article
Article
Root (mathematics)
Article By:
Lowan, Arnold N. Formerly, Department of Physics, Yeshiva University, New York, New York.
Bochner, Salomon Formerly, Department of Mathematics, Rice University, Houston, Texas.
Last reviewed:August 2020
DOI:https://doi.org/10.1036/1097-8542.593400
If a function f(x) has the value 0 for x = a, a is a root of the equation f(x) = 0. The fundamental theorem of algebra states that any algebraic equation of the form a0 xn + a1 xn−1 + 
+ an−1 x + an = 0, where the ak's are real numbers (k = 0, 1, …, n), has at least one root. From this it follows readily that such an equation has roots, real or complex, in number equal to the index (here n) of the highest power of x.
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