Derivation and Application of the Graeffe’s Roots Squaring Algorithm for the Second Order Polynomial

The goal of this study is to derive the Graeffe's root squaring algorithm for solving polynomials of the type f(x) =0. After that, the method was tested by applying it to a variety of issues found in the literature. After the fourth iteration, a comparison of the roots created by Graeffe's Root Finding Algorithm revealed that our technique provided a superior approximation nearer to the precise answer. As a result, the proposed technique in this study may be considered a more acceptable numerical strategy for solving polynomials whose exact solutions are difficult to find. For the solution of higher order polynomials, the processes for scheme derivation are simple to follow.

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