For what value of k, is −2 a zero of the given polynomial:

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

Given polynomial is: $\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}(2-3\mathrm{x})+\mathrm{k}$

As -2 is one of the zeros, the value of the given polynomial at x = -2 should be equal to zero.

Therefore,

$\mathrm{f}(-2)=0$

$\Rightarrow -2\left[2-3\left(-2\right)\right]+\mathrm{k}=0$

$\Rightarrow -2\left[2+6\right]+\mathrm{k}=0$

$\Rightarrow -16+\mathrm{k}=0$

$\Rightarrow \mathrm{k}=16$

Hence, the required value of k is 16.