SOLUTION: Find the zeros of the given function using the quadratic formula. y = 8x^4-24x^2+4

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Question 348389: Find the zeros of the given function using the quadratic formula.
y = 8x^4-24x^2+4
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
y = 8x^4-24x^2+4
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 8x%5E2%2B-24x%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=%28-24%29%5E2-4%2A8%2A4=448.

Discriminant d=448 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--24%2B-sqrt%28+448+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-24%29%2Bsqrt%28+448+%29%29%2F2%5C8+=+2.8228756555323
x%5B2%5D+=+%28-%28-24%29-sqrt%28+448+%29%29%2F2%5C8+=+0.177124344467705

Quadratic expression 8x%5E2%2B-24x%2B4 can be factored:
8x%5E2%2B-24x%2B4+=+%28x-2.8228756555323%29%2A%28x-0.177124344467705%29
Again, the answer is: 2.8228756555323, 0.177124344467705. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B-24%2Ax%2B4+%29

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= %283+%2B+sqrt%287%29%29%2F2
and = %283+-+sqrt%287%29%29%2F2