What have you tried so far?
i know how to solve the question if he didn't write that €~=0 the root would be -0.322 i took 2 points -0.5 and zero and i did the bisection method one is positive and one is negative so c=( a+b)/2 and i keep iterating ... but what does he mean €~= 0 is that suppose to mean the equation is now x^3+1??
If you are given a problem like this, surely you have learned some approximation methods. This looks like a "perturbation method" would work. Let . Then and to the third power in . The "zeroth" power of in the equation would be which has as it only real root. The "first" power of [tex]\epsilon[/b] would be or, since , so that . Do the same to find and .
Have you not seen anything like that? Are you sure you have been attending the right class? You seem to be saying that you have a whole series of problems on topics you have never seen before!