SOLUTION: Which of the following is the correct solution to the equation x^2-4x+6=0? Explain why the other solutions are wrong. a) Solution 1 x = 4±(√4^2-4•1•6)/2 x = 4±√-8/2

Algebra ->  Rational-functions -> SOLUTION: Which of the following is the correct solution to the equation x^2-4x+6=0? Explain why the other solutions are wrong. a) Solution 1 x = 4±(√4^2-4•1•6)/2 x = 4±√-8/2       Log On


   

Question 383332: Which of the following is the correct solution to the equation x^2-4x+6=0? Explain why the other solutions are wrong.
a) Solution 1
x = 4±(√4^2-4•1•6)/2
x = 4±√-8/2
x = 2±√-4
x = 2±2i
b) Solution 2
x = 4±(√4^2-4•1•6)/2
x = 4±√-8/2
x = 2±√-8
x = 2±2i√2
c) Solution 3
x = 4±(√4^2-4•1•6)/2
x = 4±√-8/2
x = 4±2i√2/2
x = 2±2i√2
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-4x%2B6+=+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=%28-4%29%5E2-4%2A1%2A6=-8.

The discriminant -8 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 -8 is + or - sqrt%28+8%29+=+2.82842712474619.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B6+%29

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x = 2 ± i*sqrt(2)
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They're wrong because they're not the correct answers.