Question

Find the zeros of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
$x^2-2x-8$

Answer 1

Given equation is $x^2-2x-8$

It can also be written as $\Rightarrow x^2-4x+2x-8$

$=x(x-4)+2(x-4)$

$=(x-4)(x+2)$

The value of $x^2-2x-8$ is zero when $x-4=0$ or $x+2=0.$

i.e, when $x=4$ or $x=-2.$

$\therefore$ The zeroes of $x^2-2x-8$ are $4$ and $-2.$

sum of zeroes $=4+(-2)=2$

product of zeroes $=-2\times 4=-8.$

Relationship between the zeroes and the coefficients for the standard quadratic equation $a{x}^2+bx+c=0$ is:

Sum of roots = $-\frac{b}{a}$ and Product of roots = $\frac{c}{a}$

In given equation

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

$a=1,b=-2,c=-8$

Sum of roots = $-\frac{-2}{1}=2$

and Product of roots = $\frac{-8}{1}=-8$

The relationship between the zeroes and the coefficients is verified.