SOLUTION: 16x^2-6x+6=0 For the equation, state the value of the discriminant and then describe the nature of the solutions. I have tried every way possible and I can't figure this out.

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Question 259766: 16x^2-6x+6=0
For the equation, state the value of the discriminant and then describe the nature of the solutions.
I have tried every way possible and I can't figure this out.
Thank you,
Patrice
Found 3 solutions by nerdybill, Alan3354, richwmiller:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
16x^2-6x+6=0
.
The "discriminant" is the stuff under the radical in the quadratic equation:
b^2 - 4ac
.
You could apply the above directly into your equation or you could have divided by 2 first.
.
6^2 - 4(16)(6)
36 - 384
-348
.
Since you have a "negative" -- the square root of a negative number would be imaginary. Therefore, you can conclude that there are "no real solutions" for this quadratic.


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
16x^2-6x+6=0
8x^2 - 3x + 3 = 0
For the equation, state the value of the discriminant and then describe the nature of the solutions.
-----------------
The onsite solver does a good job of this.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 8x%5E2%2B-3x%2B3+=+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=%28-3%29%5E2-4%2A8%2A3=-87.

The discriminant -87 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 -87 is + or - sqrt%28+87%29+=+9.32737905308882.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B-3%2Ax%2B3+%29

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
To be honest, I don't believe you that you tried everything possible.
First, do you know what the discriminant is?
Second do you know what it means when the discriminant is positive, negative or zero?
Third, did you look it up?
b^2-4ac
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 16x%5E2%2B-6x%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=%28-6%29%5E2-4%2A16%2A6=-348.

The discriminant -348 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 -348 is + or - sqrt%28+348%29+=+18.6547581061776.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B-6%2Ax%2B6+%29