Question

If one zero of the polynomial $x^2-4x+1is2+\sqrt{3}$, then find the other zero.

Answer 1

Let consider two zeros are $\alpha ,\beta$

Given, $\alpha =2+\sqrt{3}...\left(i\right)$

As we know,

Sum of the roots, $\alpha +\beta =\frac{-b}{a}=-\frac{-4}{1}=\mathrm{4...}\left(ii\right)$

Comparing $x^2-4x+1$ with general form $a{x}^2+bx+c$ we get,

$a=1,b=-4,c=1$

From equation (i) and (ii),

$2+\sqrt{3}+\beta =4\Rightarrow \beta =2-\sqrt{3}$

Hence, another roots of the given equation is $2-\sqrt{3}$