You can put this solution on YOUR website!
You can never find the complex zero of a polynomial function of any degree. That is because complex zeros always come in pairs, namely conjugate pairs of the form .
Having said that, let's find all three of the zeros of this cubic.
All cubics with rational coefficients must have at least one real zero, and it must be rational. That is because irrational zeros of polynomial equations with rational coefficients also always come in pairs.
Using the Rational Zero Theorem: If a polynomial function, written in descending order, has integer coefficients, then any rational zero must be of the form , where is a factor of the constant term and is a factor of the leading coefficient.
Examining the lead and constant coefficients of the given polynomial, we can see that the only possible rational zeros are
A bit of polynomial long division results in:
(verification of this step is left as an exercise for the student)
Therefore, is a real root of and the other two roots are also roots of
