Question:

If one zero of the polynomial $x^{2}-4 x+1$ is $(2+\sqrt{3})$, write the other zero.

Solution:

Let the other zero of the given polynomial be $\alpha$.

Now,

Sum of the zeroes of the given polynomial $=\frac{-(-4)}{1}=4$

$\therefore \alpha+(2+\sqrt{3})=4$

$\Rightarrow \alpha=4-2-\sqrt{3}=2-\sqrt{3}$

Hence, the other zero of the given polynomial is $(2-\sqrt{3})$.