The elementary symmetric polynomials of the roots must reproduce the corresponding coefficients from the polynomial that they solve, so x 1 + x 2 + x 3 = ± ± 3 n and x 1 x 2 + x 2 x 3 + x 3 x 1 = + 3 2 n 2 . Taking the ratio of these symmetric polynomials, but squaring the first so we divide out the unknown parameter n , we get a Koide-type formula: Regardless of the value of n , the solutions to the cubic equation for x must satisfy