SOLUTION: If x^4 +3x^2 + 1 = 0 then x = ?

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Question 985991: If x^4 +3x^2 + 1 = 0
then x = ?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If x^4 +3x^2 + 1 = 0
then x = ?
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Sub u for x^2
u%5E2+%2B+3u+%2B+1+=+0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation au%5E2%2Bbu%2Bc=0 (in our case 1u%5E2%2B3u%2B1+=+0) has the following solutons:

u%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=%283%29%5E2-4%2A1%2A1=5.

Discriminant d=5 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+5+%29%29%2F2%5Ca.

u%5B1%5D+=+%28-%283%29%2Bsqrt%28+5+%29%29%2F2%5C1+=+-0.381966011250105
u%5B2%5D+=+%28-%283%29-sqrt%28+5+%29%29%2F2%5C1+=+-2.61803398874989

Quadratic expression 1u%5E2%2B3u%2B1 can be factored:
1u%5E2%2B3u%2B1+=+1%28u--0.381966011250105%29%2A%28u--2.61803398874989%29
Again, the answer is: -0.381966011250105, -2.61803398874989. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B1+%29

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x%5E2+=+-3%2F2+%2B-sqrt%285%29%2F2
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x = 0%2B-sqrt%28+-3%2F2+%2B+sqrt%285%29%2F2%29
x = 0+%2B-sqrt%28+-3%2F2+-+sqrt%285%29%2F2%29