<PRE><B>Question 88437</B>
discuss the possibilities for the roots of the equation. Do not solve the equation. 
THE EQUATION IS x^5+x^3+5x=0 
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# of changes of sign for f(x) is zero
# of positive roots = zero
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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.
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Cheers,
Stan H.</PRE>