Question

If one zero of the polynomial $x^2-4x+1$ is $2+\sqrt{3}$ . Write the other zero. [CBSE 2010]

Answer 1

Let the other zeroes of $x^2-4x+1$ be a.
By using the relationship between the zeroes of the quadratic ploynomial.
We have, Sum of zeroes = $\frac{-\left(\mathrm{coefficient}\mathrm{of}\mathit{}x\right)}{\mathrm{coefficent}\mathrm{of}{x}^2}$
$$\begin{gathered} \therefore 2+\sqrt{3}+a=\frac{-\left(-4\right)}{1} \\ \Rightarrow a=2-\sqrt{3} \end{gathered}$$
Hence, the other zeroes of $x^2-4x+1$ is $2-\sqrt{3}$.