If one zero of the polynomial

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 $2-\sqrt{3}$.

 

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