If P is chosen at random in [0, 5] and the probability that the equation ${\mathrm{x}}^2+\mathrm{px}+\frac{\mathrm{p}+2}{4}=0$has real roots is $\frac{\mathrm{\lambda }}{10}\text{ then }\mathrm{\lambda }=$

Roots of${\mathrm{x}}^2+\mathrm{px}+\left(\frac{\mathrm{p}+2}{4}\right)=0\text{ are real if }\mathrm{\Delta }\ge 0$
$\Rightarrow {\mathrm{p}}^2-\mathrm{p}-2\ge 0\Rightarrow \mathrm{p}\le -1\text{ or }\mathrm{p}\ge 2\text{ where }\mathrm{p}\in [0,5]$

n(S)= length of the interval$[0,5]$=5

n(E)=$$\begin{gathered} \mathrm{p}\ge 2\text{ where }\mathrm{p}\in [0,5] \\ \Rightarrow p\in \left[2,5\right] \end{gathered}$$
$\therefore$Required probability
$$\begin{gathered} =\left[\frac{\text{ favourable length }}{\text{ total length }}\right]=\frac{3}{5}=\frac{\mathrm{\lambda }}{10}\left(\text{ given }\right) \\ \Rightarrow \lambda =6 \end{gathered}$$