The number of positive integral values of ‘k’ for which $y=f\left(x\right)$  where $f\left(x\right)=\left(16x^2+12x+39\right)+k\left(9x^2-2x+11\right)$ . Touches $x-\text{axis}$ , is

$\therefore {\text{b}}^2-4ac=0$

${\left(12-2k\right)}^2-4\left(16+9k\right)\left(39+11k\right)=0$

$\Rightarrow 99k^2+407k+588=0$

$\frac{-b}{a}=\frac{-407}{99}<0$

$\frac{c}{a}=\frac{588}{99}>0$

In above equation both roots are negative

$\therefore$  Number of positive integral values of $k\text{ is }0$