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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Updated on: 10-Oct-2022

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