SOLUTION: 4x _______ x4 + 4x2 + 4 = 0

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Question 1007707: 4x
_______
x4 + 4x2 + 4 = 0
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
4x
_______
x4 + 4x2 + 4 = 0

The equation looks like (4x)/(x^4+4x^2)+4=0
rendered as %284x%29%2F%28x%5E4%2B4x%5E2%29%2B4=0.

4x%2F%28x%5E4%2B4x%5E2%29%2B4%28x%5E4%2B4x%5E2%29%2F%28x%5E4%2B4x%5E2%29=0
%284x%2B4%28x%5E4%2B4x%5E2%29%29%2F%28x%5E4%2B4x%5E2%29=0
And the numerator is now what is important to equate to 0.

4x%2B4x%5E4%2B16x%5E2=0
4x%5E4%2B16x%5E2%2B4x=0
x%5E4%2B4x%5E2%2Bx=0
x%28x%5E3%2B4x%2B1%29=0

The degree three factor has no apparent rational roots, as checked with Rational
Roots Theorem and synthetic division. There is a root of 0 for the factor x.

The rational term in the original equation can be negative. x%3C%3E0 because that value will make the
denominator become 0, not allowed.

NO SOLUTION
A graphing program will show a root, not rational, near -0.2462.