Find a rational zero of the polynomial function and use it to find all the zeros of the function.
f(x) = x^4 + 3x^3 - 5x^2 - 9x - 2

Question

Find a rational zero of the polynomial function and use it to find all the zeros of the function.
 f(x) = x^4 + 3x^3 - 5x^2 - 9x - 2

mathmale · Answer

A rational zero is an x value that can be expressed as the ratio of two integers, such as 2/3.  This would rule out a zero such as Sqrt(5) (which is not rational).

Set f(x) = to 0.  Your next job is to solve this for x.  Expect four roots, since this polynomial is of the fourth degree.  Which methods of finding roots of polynomials are more familiar to you?  Have you experienced "synthetic division?"  Factoring by grouping?  Graphing?

mathmale · Answer

Still want to discuss this problem?  Happy to, if you do.  It's been 21 days.