Answer: Positive real zeros- 2 or 0
Negative real zeros - 2 or 0
Complex zeros-4 or 2 or 0
Step-by-step explanation:
Given: A fourth degree polynomial [tex]f(x)=8x^4+13x^3-11x^2+x+9[/tex] is arranged in descending order already .
We can see that it has two sign change from second to third term and then third to fourth ,so by Descartes rules of signs it has 2 or zero positive real roots.
Now [tex]f(-x)=8x^4-13x^3-11x^2-x+9[/tex] [change signs of coefficient with odd degree of x]
Here we have two sign change from first to the second term and from fourth to the constant term.
Therefore by Descartes rules of signs f(x) has 2 or zero negative real roots.
As it is 4th degree polynomial so it can have 4 roots and complex roots occur in pair so f(x) can have 4 or 2 or 0 complex roots.
