f(x)=x^3+2x^2-x+k dtermina los intervalos de positividad y negatividad usando el cuadro con los signos

Sorry, I don't speak Spanish. But if you want a solution for x, then here it's:

 

x = (3 sqrt(3) sqrt(27 k^2+68 k-8)-27 k-34)^(1/3)/(3 2^(1/3))+(7 2^(1/3))/(3 (3 sqrt(3) sqrt(27 k^2+68 k-8)-27 k-34)^(1/3))-2/3

 

Hope you can understand some English.