SOLUTION: compute the discriminant. then determine the number and type of solutions for the given equation. 7x2-4x+4=0 what is the discriminant?

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Question 302204: compute the discriminant. then determine the number and type of solutions for the given equation.
7x2-4x+4=0
what is the discriminant?
Found 2 solutions by Alan3354, nerdybill:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The onsite solver covers that.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 7x%5E2%2B-4x%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=%28-4%29%5E2-4%2A7%2A4=-96.

The discriminant -96 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 -96 is + or - sqrt%28+96%29+=+9.79795897113271.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+7%2Ax%5E2%2B-4%2Ax%2B4+%29

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
compute the discriminant. then determine the number and type of solutions for the given equation.
7x2-4x+4=0
what is the discriminant?
.
Given the quadratic:
ax^2 + bx + c = c
then the "discriminant" is:
b^2 - 4ac
.
So, for your equation:
7x^2-4x+4=0
b^2 - 4ac
= (-4)^2 - 4(7)(4)
= 16 - 4(7)(4)
= 16 - 112
= -96
.
Since it is negative: No real solutions
(two imaginary solutions)
.
For additional info:
http://www.mathwarehouse.com/quadratic/discriminant-in-quadratic-equation.php