Write a quadratic polynomial, sum of whose zeros is

As we know that the quadratic polynomial $f(x)=k\left[x^{2}-(\right.$ sum of their roots $) x+($ product of their roots $\left.)\right]$

According to question,

(sum of their roots) $=2 \sqrt{3}$

And (product of their roots) $=2$

Thus putting the value in above,

$f(x)=k\left[x^{2}-2 \sqrt{3} x+2\right]$ where $k$ is real number.

Therefore, the quadratic polynomial be

$f(x)=k\left[x^{2}-2 \sqrt{3} x+2\right]$