Question 977336
f(x) has one real but IRRATIONAL root.  The value is very near {{{-0.71}}}.  You would have to use some numerical testing to find the value for the accuracy you want.  Use the idea that this real (but irrational) root is where f(x) will change signs.  Near -0.71, to the left is one sign and to the right is the opposite sign.  Keep checking with whatever numeric method you want, for as much accuracy as you require.


When you have your best value for this real, irrational root, then use synthetic division to get the corresponding coefficients of the quadratic factor resulting for the quotient.  Solve THAT for ITS <b>complex</b> roots.  (General Solution Method for Quadratic Equation).


A graphing tool zoomed in several levels indicates  the irrational real root about  {{{-0.7097}}}; and you might zoom in further for a better accurate value.