11.42 Does the equation $x^{3}+2 x-3=0$ have negative roots?
11.42 Method I. Factoring the left side of the equation, we get $(x-1)\left(x^{2}+x+3\right)=0$. Since $x^{2}+x+3>0$ for any $x$, then $x-1=0$, from which $x=1$. Therefore, the equation has no negative roots.

Method II. We will solve the given equation graphically. Writing it in the form $x^{3}=-2 x+3$, we will plot the graphs of the functions $y=x^{3}$ and $y=-2 x+3$ (Fig. 11.15). Using the graph, we establish that $x=1>0$ and there are no other roots.

Answer: no.