SOLUTION: Determine the nature of the solutions of the equation: Does it have 1 real solution, 2 real solutions, or 2 non real solutions? x^2 - 8x + 16 = 0 (-8)^2 -16*x*16= 64-256 The

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Determine the nature of the solutions of the equation: Does it have 1 real solution, 2 real solutions, or 2 non real solutions? x^2 - 8x + 16 = 0 (-8)^2 -16*x*16= 64-256 The       Log On


   

Question 233413: Determine the nature of the solutions of the equation:
Does it have 1 real solution, 2 real solutions, or 2 non real solutions?
x^2 - 8x + 16 = 0
(-8)^2 -16*x*16= 64-256
The answer 2 non real solutions? I think I went wrong somewhere.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Does it have 1 real solution, 2 real solutions, or 2 non real solutions?
x^2 - 8x + 16 = 0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-8x%2B16+=+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=%28-8%29%5E2-4%2A1%2A16=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%28-8%29%29%2F2%5C1.
Expression can be factored: 1x%5E2%2B-8x%2B16+=+%28x-4%29%2A%28x-4%29

Again, the answer is: 4, 4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-8%2Ax%2B16+%29

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It has a double solution at x = 4. 4 is a real number --> 1 real