If a cubic polynomialwhere
is real, has a real root and two purely complex roots, we can find the value of
and the complex roots by deriving simultaneous equations.
Since the coefficients of the polynomial are real, the purely complex rootsand
occur as a complex conjugate pair so that we can write
and
If the real root is
the the polynomial can be written as
Then from considering the coefficients of
(1)
(2)
and the constant term gives(3)
(3) divided by (2) gives
Then from (1)
Then from (2),
Then