Answer:
5
2
2
Step-by-step explanation:
Given in the question the polynomial
x^5 - 9x^4 + 13x³ + 57x² - 86x - 120
1)
has total of 5 zeroes
Regardless of odd or even, any polynomial of positive order can have a maximum number of zeros equal to its order.
2)
maximum of 2 positive real roots
Using Descartes' Rule of Signs
x^5 - 9x^4 + 13x³ + 57x² - 86x - 120
------------ -----------
1 2
There are 2 sign changes in the positive-root case. This number 2 is the maximum possible number of positive zeroes.
3)
maximum of 2 negative real roots
Using Descartes' Rule of Signs
When f (–x), we have
- x^5 - 9x^4 - 13x³ + 57x² + 86x - 120
--------- ----------
1 2
number of sign changes = 2
