Question

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficient.
$x^2-2x-8$

Answer 1

Let us first find the zeroes of the given polynomial $x^2-2x-8$ by equating it to $0$ as shown below:

$x^2-2x-8=0\Rightarrow x^2-4x+2x-8=0\Rightarrow x(x-4)+2(x-4)=0\Rightarrow (x+2)(x-4)=0\Rightarrow (x+2)=0,(x-4)=0\Rightarrow x=-2,x=4$

Therefore, the zeroes are $-2$ and $4$.

In the polynomial $x^2-2x-8$, we have $a=1,b=-2$ and $-8$. Now, consider

Sum of zeroes

$-2+4=2=-\frac{(-2)}{1}=-\frac{b}{a}$

Product of zeroes

$-2\times 4=-8=-\frac{8}{1}=\frac{c}{a}$

Hence, the relation between the zeroes and coefficients is verified.