Question

find the root for 2x^3+5x^2+6x+2=0

Answer 1

there are no positive roots for sure
if there are negative ones, they must be either \(-1,-2\) or \(-\frac{1}{2}\) or else they are irrational
try \(-1\) first

Answer 2

Hopefully it's obvious that any real root must be negative, as all the terms have positive coefficients. @satellite73's suggestions are brought to you by the rational root theorem, in case you're wondering how he could know that.