ROUTINE FOR FINDING ROOTS OF POLYNOMIALS WITH REAL COEFFICIENTS

A routine that computes the real and the complex roots of polynomials with real coefficients up to the tenth degree is reported. In case of an even polynomial it computes its quadratic factors and solves each factor by the quadratic formula. In case of an odd polynomial it computes one real root by locating it and refining by Newtons algorithm. Then it removes the computed root from the polynomial reducing its degree by one. The reduced polynomial is of even degree and it is solved by quadratic factors. The routine fails when a the real roots are of even multiplicity, converging then to wrong values, bREAL ROOTS ARE OF ODD MULTIPLICITY, NOT CONVERGING AT ALL, c the polynomial is badly conditioned very small changes in coefficients cause large changes in the values of the roots converging then to wrong values. The routine is planned to compute frequencies in vibrations problems which involve complex roots. Statistical evidence seems to indicate that only polynomials with real roots can be badly conditioned. If this were the case the handicap c would be of minor importance only.