Why does

(2-X)^2=-1

have no real solution?

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- Jun 6th 2009, 07:51 PMprettiestfriendQuadratics question
Why does

(2-X)^2=-1

have no real solution? - Jun 6th 2009, 07:53 PMJoel
This is because no number squared either positive or negative can give a negative answer.

- Jun 6th 2009, 08:10 PMyeongil
And I'll be willing to bet that many math students, when seeing this problem, would expand the (2 - x)^2 and try to solve for x using the quadratic formula. It drives me nuts when students make problems much harder than they have to be.

01 - Jun 6th 2009, 09:40 PMProve It
But that's not to say that doing that wouldn't work...

$\displaystyle (2 - x)^2 = -1$

$\displaystyle 4 - 4x + x^2 = -1$

$\displaystyle x^2 - 4x + 5 = 0$

Now checking the discriminant gives...

$\displaystyle \Delta = (-4)^2 - 4\times 1\times 5$

$\displaystyle = 16 - 20$

$\displaystyle = -4 < 0$.

So no solution exists.

Having said that - you are right, it IS easiest to just notice that you can not square any real number to get a negative result. - Jun 6th 2009, 10:22 PMaidan