SOLUTION: Find the Solution set of the equation e^5x+4e^3x+4e^2x=-9-3e^x+5e^4x

Question 1037153: Find the Solution set of the equation e^5x+4e^3x+4e^2x=-9-3e^x+5e^4x
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!

<==> .
Now let .
Then the last equation is equivalent to
.
By using the rational root theorem and trying out root candidates by synthetic division, you will find that --
.
==> the zeros are w = -1, 3 (double), i, -i.
Therefore the solution set of the original equation is { ln(-1), ln3, ln3, lni, ln(-i)}
If we are after REAL zeros only, then the solution to the original equation is x = ln3, which is a double root. ( ln(-1), lni, and ln(-i) all have values in the complex domain.)

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