State whether the following quadratic equations have two distinct real roots. Justify your answer.
$ (x+4)^{2}-8 x=0 $

Given:

\( (x+4)^{2}-8 x=0 \)

To do:

We have to state whether the given quadratic equations have two distinct real roots.

Solution:

\( (x+4)^{2}-8 x=0 \)

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

$x^2+8x-8x+16=0$

$x^2+16=0$

Comparing with $a x^{2}+b x+c=0$, we get,

$a =1, b=0$ and $c=16$

Discriminant $D=b^{2}-4 a c$

$=(0)^{2}-4(1)(16)$

$=0-64$

$=-64<0$

$D<0$

Hence, the equation \( (x+4)^{2}-8 x=0 \) has no real roots.