Question

Find the zeroes of the following quadratic polynomial and verify.
$x^2+4x+4$

Answer 1

Factorise the given polynomial $x^2+4x+4$ as shown below:

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

Therefore, the zeroes of the polynomial is $x=-2,-2$.

The sum and product of the zeroes is:

Sum$=-2+(-2)=-2-2=-\mathrm{4.........}\left(1\right)$

Product$=(-2)\times (-2)=\mathrm{4.......}\left(2\right)$

Now, in general, we know that for a equation $a{x}^2+bx+c=0$, if zero are $\alpha$ and $\beta$, plug the values of $a$, $b$ and $c$ we get,

Sum and product of the zeroes is:

Sum$=-\frac{b}{a}=-\frac{4}{1}=-\mathrm{4.......}\left(3\right)$

Product$=\frac{c}{a}=\frac{4}{1}=\mathrm{4........}\left(4\right)$

Thus, equation 1 is equal to equation 3 and equation 2 is equal to equation 4.

Hence verified.