If x = 2 is a root of the polynomial $\mathrm{f}\left(\mathrm{x}\right)=2{\mathrm{x}}^2-3\mathrm{x}+6\mathrm{a}$, then find the value of a.

$\mathrm{f}\left(\mathrm{x}\right)=2{\mathrm{x}}^2-3\mathrm{x}+6\mathrm{a}$

Given, x = 2 is the root of the polynomial.

i.e. f(2) = 0.

∴  $\mathrm{f}\left(2\right) = 2{\left(2\right)}^2-3\left(2\right)+6\mathrm{a} = 0$

$\Rightarrow 8-6+6\mathrm{a} = 0$

=> 6a = - 2

$\Rightarrow \mathrm{a} = -\frac{2}{6}$

$\Rightarrow \mathrm{a} = -\frac{1}{3}$