SOLUTION: xcubed minus xsquard+x-1=0 find the complex zero

Question 199397This question is from textbook Algebra 2 with trigonometry
: xcubed minus xsquard+x-1=0 find the complex zero This question is from textbook Algebra 2 with trigonometry

Answer by solver91311(24713) (Show Source): 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