APPROXIMATE DETERMINATION OF POLYNOMIAL ROOTS
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Abstract
Three theorems are given for approximate determination of magnitudes of polynomial roots. A definition for the order of a number is given first. The first theorem is for a polynomial equation with all coefficients the same order of magnitude. The second theorem deals with polynomial equations having only one coefficient of different magnitude from the others. Finally, the third theorem is a general theorem valid for any arbitrary polynomial equations. The theorems successfully determine the magnitudes of roots for arbitrary degree of polynomial equations. An additional fourth theorem predicts the roots for the special case of two dominant terms in the polynomial. Proofs and numerical applications of each theorem are presented. It is shown that the predictions of the theorems and the real roots are in reasonable agreement.