Iterative methods provide an alternative to finding the solutions of equations where analytical methods are inconvenient or even impossible to use. This study which focuses on cubic polynomial equation f (t) = at 3 + bt 2 + ct + d = 0, a > 0 with real coefficients and having an imaginary root, found that the fixed-point iterationwill always converge to the real part x of the imaginary root of f (t) = 0 whenever b 2 -3ac < 0. The only real root of g(t) = ½ f (t) f (t) -af (t) = 0 was found to be the real part x of the imaginary root of f (t) = 0 and is always outside the interval formed by the critical numbers of the function f.
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