SOLUTION: Find all solution of the equation algebraically 9u^2/3+12u^1/3+4=0

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Question 354414: Find all solution of the equation algebraically
9u^2/3+12u^1/3+4=0
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
9u^2/3+12u^1/3+4=0
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Sub x for u^(1/3)
9x^2 + 12x + 4 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 9x%5E2%2B12x%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=%2812%29%5E2-4%2A9%2A4=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%2812%29%29%2F2%5C9.
Expression can be factored: 9x%5E2%2B12x%2B4+=+%28x--0.666666666666667%29%2A%28x--0.666666666666667%29

Again, the answer is: -0.666666666666667, -0.666666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B12%2Ax%2B4+%29

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x = -2/3
u^(1/3) = -2/3
u = -8/27