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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.
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