Question

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

Answer 1

To find another zero of the polynamial $x^2-4x+1$ , if one of them will be $\left(2+\sqrt{3}\right)$

let consider two zeros $\alpha ,\beta$

$\alpha =2+\sqrt{3}\left(given\right)$

$\alpha +\beta =-\frac{b}{a}$

$\alpha +\beta =\frac{-\left(-4\right)}{1}$

$\left(x^2-4x+1comparingwithgenaralequationa{x}^2+bx+c,thena=1,b=-4,c=1\right)$

$\alpha +\beta =4$

$fromequation\left(1\right)\&\left(2\right)$

$\alpha +\beta =4$

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

$\beta =4-\left(2+\sqrt{3}\right)$

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

$\beta =2-\sqrt{3}$