Polynomial root-finding
Finding the roots of polynomials is a long-standing problem that has been extensively studied throughout the history and substantially influenced the development of mathematics. It involves determining either a numerical approximation or a closed-form expression of the roots of a univariate polynomial, i.e., determining approximate or closed form solutions of x {\displaystyle x} in the equation a 0 + a 1 x + a 2 x 2 + ⋯ + a n x n = 0 {\displaystyle a_{0}+a_{1}x+a_{2}x^{2}+\cdots +a_{n}x^{n}=0} where a i {\displaystyle a_{i}} are either real or complex numbers.