Question:
Write a quadratic polynomial, sum of whose zeros is $2 \sqrt{3}$ and their product is 2 .
Solution:
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
$f(x)=k\left[x^{2}-2 \sqrt{3} x+2\right]$