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Theory: In order to extract a real or complex root of a polynomial, Bairstow's method given in the year 1920, attempts to extract a quadratic factor of the polynomial equation, Bairstow method, Convergence of the method. Developed by For example, to find the poles, singularities, etc. of a.A novel method is proposed for real polynomials that does not require any complex arithmetic within iterations. It is based on the observation that Aberth's Bairstow Method is an iterative method used to find both the real and complex roots of a polynomial. It is based on the idea of synthetic division. xn + a1 xn-1 + . . . + an-1x + an = 0 · (x2 + px + q) Qn-2(x) + Rx + S = 0 · xn-2 + b1 xn-3 + . . . + bn-3x + bn-2 = 0,. Example-1. Find all roots of polynomial using Bairstow method f(x) = x^4-3x^3+3x^2-3x+2 and r = 0.1, s = 0.1. Solution: Let the initial approximation be and Lin-Bairstow Method. • Algorithm. – m > 3: determine quadratic roots, reduce order of problem by 2. – m = 3: determine linear root then quadratic roots.