Find the zeroes of the polynomial $f(x)=x^{2}-2 x-8$ and verify the relation between its zeroes and coefficients.
Find the zeroes of the polynomial $f(x)=x^{2}-2 x-8$ and verify the relation between its zeroes and coefficients.

$x^{2}-2 x-8=0$

$\Rightarrow \mathrm{x}^{2}-4 \mathrm{x}+2 \mathrm{x}-8=0$

$\Rightarrow x(x-4)+2(x-4)=0$

$\Rightarrow(x-4)(x+2)=0$

$\Rightarrow(x-4)=0$ or $(x+2)=0$

$\Rightarrow x=4$ or $x=-2$

Sum of zeroes $=4+(-2)=2=\frac{2}{1}=\frac{-(\text { coefficient of } x)}{\left(\text { coefficient of } x^{2}\right)}$

Product of zeroes $=(4)(-2)=\frac{-8}{1}=\frac{\text { constant term }}{\left.\text { (coefficient of } x^{2}\right)}$