Question

Type the correct answer in the box

Answer 1

5

2

2

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