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State whether the following quadratic equations have two distinct real roots. Justify your answer.
$ (x-1)(x+2)+2=0 $
Given:
\( (x-1)(x+2)+2=0 \)
To do:
We have to state whether the given quadratic equations have two distinct real roots.
Solution:
$(x-1)(x+2)+2=0$
$x^{2}+x-2+2=0$
$x^{2}+x+0=0$
Comparing the above equation with $a x^{2}+b x+c-0$, we get,
$a=1, b=1$ and $c=0$
Therefore,
Discriminant $D=b^{2}-4 a c$
$=1-4(1)(0)$
$=1>0$
$D>0$
Hence, the equation $(x-1)(x+2)+2=0$ has two distinct real roots.
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