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9 n n 9 n Zx 9abc absolute value accurate value adverse sign Cardan's solution choosing the signs conjugate complex numbers conjugate complex roots correct to six corresponding value cube root cubic equations equals the third equation x3 Extracting the cube formula for Y2 further accuracy imaginary terms ir(Z+l method Multiplying n n n n n Zl n Zl n obtain the three Obtain Z2 Properly choosing radical sign real root real term reduce the equation roots are real rules It follows sign as q sign is negative sign of q six decimal places solution of cubic solving a cubic Substituting the values Szx2 table obtain term is bounded three roots three values value is greater value of zx whence z2 and z3 z3 are conjugate z3 is positive Zi n Zi Zl n n Zl n Zl zx increases zx n zx