Question 1044584
Try Rational Roots Theorem.


{{{x^3+x^2-x-3=0}}}
Possible roots to check for are -3, -1, 1, 3; and you could expect possibly to find three roots.


<pre>

-3    |    1   1   -1   -3
      |
      |       -3   6    -15
      |___________________________
          1   -2    5   -18

-1    |    1    1    -1    -3
      |
      |        -1     0     1
      |_________________________
           1   0    -1     -2

 1    |    1    1    -1    -3
      |
      |         1    2     1
      |_____________________________
           1    2    1    -2

  3    |     1    1    -1     -3
       |
       |          3   12      33
       |_______________________________
            1     4    11     36
</pre>
No rational zeros found.  A real zero seems to be between x values of 1 and 3 but finding it or them requires an approximation method.


If you try a graphing tool, you will find a root or zero at close to {{{x=1.358}}}.  This will be the ONLY real root.