3x^3 -15x^2 -13x-4

Question

what are the zeros of this problem?

Answer 1

when x=6 the expression is positive,
when x=5 it is negative, so there is a zero between 5 and 6

I ran it trough my homemade equation solver and got x = appr. 5.788

reducing the expression using synthetic division resulted in two imaginary roots.

So the expression has one real zero at about x = 5.788

Answer 2

The "p/q theorem" says that if there is any real rational root, it will be + or - p/q, where p and q are prime factors of the first and last terms, which are 3 and 1 for p and 1,2 and 4 for q. I can't find any p/q ratios that work, so a graphical or iterative (trial and error) solution may be required.