Expert: Richard J. Raridon - 6/5/2004

Question
Thanks for you help with my last question - feels wonderful to make some progress. Now I am now stuck on the negative real roots of a polynomial. I was able to digest the positive roots. Here are the two problems in question

Determine the number of possible negative real roots of the polynomial:

5x^4-6x^3+4x^2-9x+10

I believe the answer is either 2 or 2 and zero?
Second problem:

-3x^4+5x^3+8x^2-7x+2

Again not sure whether zero is one of the possible answers.

Thanks  

Answer
Re-write the expression as
f(x) = 5x^4 -6x^3 +4x^2 -9x +10
try a value for x.  If it is a solution, f(x) will = 0.  
In this case, f(0) = 10; f(1) = 4; f(2) = 40, f(-1) = 34
Since it appears that f(x) is positive for any value of x, there are no real roots, only imaginary ones.  
The same is true for the second expression.