SOLUTION: solve x2 - x + 1 I tried by using quadratic formula.

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Question 468507: solve x2 - x + 1
I tried by using quadratic formula.
Found 2 solutions by jorel1380, algebrahouse.com:
Answer by jorel1380(3719)   (Show Source): You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

The discriminant -3 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -3 is + or - .

The solution is

Here's your graph:
Answer by algebrahouse.com(1659)   (Show Source): You can put this solution on YOUR website!
xČ - x + 1 = 0
a = 1, b = -1, c = 1

-b ± √(bČ - 4ac)
---------------- = x {the quadratic formula}
2a

-(-1) ± √[(-1)Č - 4(1)(1)]
--------------------------- = x {substituted into quadratic formula}
2(1)

1 ± √(1 - 4)
------------- = x {simplified}
2

1 ± √-3
--------- = x {subtracted 1 and -4}
2

1 ± √-1 √3
----------- = x {broke the -3 into -1 and 3, because you can't take square root of negative number}
2

1 ± i√3
-------- = x {using imaginary numbers, the square root of -1 is i}
2

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