If values of m for which the line $\mathrm{y}=\mathrm{mx}+2\sqrt{5}$ touches the hyperbola $16{\mathrm{x}}^2-9{\mathrm{y}}^2=144$ are roots of the equation ${\mathrm{x}}^2-(\mathrm{a}+\mathrm{b})\mathrm{x}-4=0$, then value of (a + b) is equal to

$\begin{array}{l}Given hyperbola \frac{x^2}{9}-\frac{y^2}{16}=1\\ where a^2=9,b^2=16\\ Given y=mx+2\sqrt{5} is \tan gent to the given hyperbola\\ then c^2=a^2{m}^2-b^2\\ \Rightarrow 20=9m^2-16\\ \Rightarrow 9m^2=36\\ \Rightarrow m^2=4\\ \Rightarrow m=\pm 2\\ Now 2 and -2 are roots of the equation x^2-(a+b)x-4=0\\ \Rightarrow sum of roots =2-2=0\\ \therefore \mathrm{a}+\mathrm{b}=0\end{array}$