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State whether the following quadratic equations have two distinct real roots. Justify your answer.
$ x(1-x)-2=0 $
Given:
\( x(1-x)-2=0 \)
To do:
We have to state whether the given quadratic equations have two distinct real roots.
Solution:
$x(1-x)-2=0$
$x^{2}-x+2=0$
Comparing with $a x^{2}+b x+c=0$, we get,
$a=1, b=-1$ and $c=2$
Therefore,
Discriminant $D=b^{2}-4 a c$
$=(-1)^{2}-4(1)(2)$
$=1-8$
$=-7<0$
$D<0$
Hence, the equation $x(1-x)-2=0$ has no real roots.
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