SOLUTION: Hello I am working with the Descartes rule of signs. I am supposed to discuss the possibilities for the roots of the equation. Do not solve the equation. THE EQUATION IS x^5+

Question 88437: Hello I am working with the Descartes rule of signs.
I am supposed to discuss the possibilities for the roots of the equation. Do not solve the equation.
THE EQUATION IS x^5+x^3+5x=0
Here is my answer
Pos: 3......0
Neg: 0......3
Imag:
Am I even close on this problem?
Thank you
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
discuss the possibilities for the roots of the equation. Do not solve the equation.
THE EQUATION IS x^5+x^3+5x=0
---------
# of changes of sign for f(x) is zero
# of positive roots = zero
---------
f(-x)=-x^5-x^3-5x
# of changes of sign of f(-x) is zero
# of negative roots = 0
The equation can be written as x(x^4+x^2+5)=0
So, it has a zero at x=0.
The remaining four roots are imaginary.
==============
Cheers,
Stan H.
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