Question:
If one zero of the polynomial $x^{2}-4 x+1$ is $2+\sqrt{3}$. Write the other zero.
Solution:
Let the other zeroes of $x^{2}-4 x+1$ be $a$.
By using the relationship between the zeroes of the quadratic ploynomial.
We have, Sum of zeroes $=\frac{-(\text { coefficient of } x)}{\text { coefficent of } x^{2}}$
$\therefore 2+\sqrt{3}+a=\frac{-(-4)}{1}$
$\Rightarrow a=2-\sqrt{3}$
Hence, the other zeroes of $x^{2}-4 x+1$ is $2-\sqrt{3}$.