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 a₀xⁿ + a₁xⁿ⁻¹ + … + a_n−1x + a_n = 0, where the a_k'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.