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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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