Question 252309
Let's look at this using Descartes rule of signs. X = 4 and X = -2 will generate roots.
X = 4 divides the original polynomial with an answer of: {{{2X^3 + 5X^2 + 6X + 2}}}
X = -1/2 divides the second polynomial with an answer of:  {{{2X^2 + 4X + 4 }}}
Set this polynomial = 0 and use quadratic. We get X = {{{-1 +- isqrt(2)}}}