If ${\mathrm{x}}^2+3\mathrm{x}+5=0\text{ and }{\mathrm{ax}}^2+\mathrm{bx}+2=0$ have a common root and $\mathrm{a},\mathrm{b}\in \mathrm{R}$, then the value of a + b is equal to $\frac{\mathrm{k}}{5},$ then k =

The given equations are  ${\mathrm{x}}^2+3\mathrm{x}+5=0\text{ and }{\mathrm{ax}}^2+\mathrm{bx}+2=0$ 

and its have a common root,

Imaginary roots occur in conjugate pairs $\Rightarrow$ both roots are common

$\therefore \frac{\mathrm{a}}{1}=\frac{\mathrm{b}}{3}=\frac{2}{5};\therefore \mathrm{a}=\frac{2}{5}\text{ and }\mathrm{b}=\frac{6}{5}$

$\therefore \mathrm{a}+\mathrm{b}=\frac{8}{5}$.