SOLUTION: What are the possible number of positive, negative and imaginary zeros of: f(x)= x^3 - 11x^2 + 8x - 20

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Question 1180205: What are the possible number of positive, negative and imaginary zeros of:
f(x)= x^3 - 11x^2 + 8x - 20

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=+x%5E3+-+11x%5E2+%2B+8x+-+20
Use Decartes' rule of signs...
So, the coefficients are 1,-11,8,-20
As can be seen, there are 3+changes.
This means that there are 3+or 1+positive real roots.
To find the number of negative real roots, substitute x with -x in the given polynomial:
x%5E3+-+11x%5E2+%2B+8x+-+20 becomes -x%5E3+-+11x%5E2+-+8x+-+20
The coefficients are -1,-11,-8,-20.
As can be seen, there are+0 changes.
This means that there are+0 negative real roots.
Answer:
3 or 1 positive real zeros
0 negative real zeros
0 or 2 imaginary zeros