Question

Very-Short-Answer Questions

If one zero of the polynomial $x^2-4x+1$ is $\left(2+\sqrt{3}\right)$, write the other zero. [CBSE 2010]

Answer 1

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

Now,
Sum of the zeroes of the given polynomial = $\frac{-\left(-4\right)}{1}$= 4
$$\begin{gathered} \therefore \alpha +\left(2+\sqrt{3}\right)=4 \\ \Rightarrow \alpha =4-2-\sqrt{3}=2-\sqrt{3} \end{gathered}$$

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