Question 12
Let $g(x)=x^3+3x^2-x-5$ and suppose that $\alpha_1,\alpha_2,\alpha_3$ are the three distinct real roots of $g(x)$, where $\alpha_1\lt \alpha_2\lt \alpha_3$. Find $|\lfloor\alpha_1\rfloor|+|\lfloor\alpha_2\rfloor|+|\lfloor\alpha_3\rfloor|$.