SOLUTION: Im not sure if this is available through this website, but if you can, can you please help me? i have a test tomorrow. Given the polynomial function: f(x)={{{ 4x^2-4x+1 }}}

Algebra ->  Test -> SOLUTION: Im not sure if this is available through this website, but if you can, can you please help me? i have a test tomorrow. Given the polynomial function: f(x)={{{ 4x^2-4x+1 }}}       Log On


   

Question 369495: Im not sure if this is available through this website, but if you can, can you please help me? i have a test tomorrow.
Given the polynomial function: f(x)=+4x%5E2-4x%2B1+
Find the zeroes of f(x) algebraically.
Write f(x) as a product of its linear factors.
Even if you can't answer thankyou for reading this. Have a nice day
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=+4x%5E2-4x%2B1+=+0
%282x-1%29%5E2+=+0
(2x-1)*(2x-1) = 0
2x = 1
x = 1/2 is the answer, multiplicity 2
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There are 2 answers, both of them are x = 1/2
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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 4x%5E2%2B-4x%2B1+=+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%2A4%2A1=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%28-4%29%29%2F2%5C4.
Expression can be factored: 4x%5E2%2B-4x%2B1+=+%28x-0.5%29%2A%28x-0.5%29

Again, the answer is: 0.5, 0.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-4%2Ax%2B1+%29

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Ignore the comments about 1 solution. There's one value for the 2 solutions.