SOLUTION: find x intercepts y=x^2-2x+4 could you show all steps i am having a hard time with this

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Question 43678: find x intercepts y=x^2-2x+4 could you show all steps i am having a hard time with this
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+x%5E2+-+2x+%2B+4
0+=+x%5E2+-+2x+%2B+4
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%282+%2B-+sqrt%28+%28-2%29%5E2+-+4%2A1%2A4+%29%29%2F%282%29+
x+=+%282+%2B-+sqrt%28+%28-2%29+-+16+%29%29%2F%282%29+
x+=+%282+%2B-+sqrt%28+-12+%29%29%2F%282%29+
x+=+1+%2B-+i%2Asqrt%283%29+ There are no x-intercepts.
+graph%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C+x%5E2+-+2x+%2B+4+%29+
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B4+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-2%29%5E2-4%2A1%2A4=-12.

The discriminant -12 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 -12 is + or - sqrt%28+12%29+=+3.46410161513775.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B4+%29