What is the probability that the roots of the equation x^2+x+n=0...

A quadratic equation has only two roots. Here, $x^2+x+n=0$ and $n \in \mathbb{N}$ where $n < 4\therefore n=1,2,3 \Rightarrow$ Three equations are possible. Thus, Total number of Roots, $n=6\rightarrow$ For equation $x^2+x+n=0 ; \mathrm{D}=1-4 n\mathrm{D} < 0$ when $n=1,2$ and 3 $\therefore$ Equation will give complex roots not real. Thus, favourable number of roots, $r=0$ Hence, probability $=\frac{r}{n}=\frac{0}{6}=0$