1) what are the real zeroes of x3 + 6 x2 – 9x – 54?
a. 1, 2, 27
b. 3, -3, -6
c. -6, 3, -6
d. 2, -1, 18
e. 3, 3, -6
2) an entrepreneur estimates that the total profit (profit = total revenue minus total cost) from his proposed company will be given by the function p(x) = x3 – 4x2 + 3x – 12,
where p is in hundreds of dollars and x is the number of years elapsed after the company starts operations. in how many years (x) will the company break even
(no profit, no loss)?
a. 1 year
b. 2 years
c. 3 years
d. 4 years
e. 6 years
3)how many negative roots can this polynomial function possibly have?
f(x) = 5x4 – 7x3 – x2 – 3x – 2
a. 1
b. 5 or 3 or 1
c. 3 or 1
d. 4 or 2 or 0
e. 2 or 0

Question 1)

The polynomial function is:

It could be written as:

The roots of a function are the possible values of x where f(x)=0

i.e.

Since,

Hence, we get:

Hence, the real zeros of the given problem is:

       B.   3, -3, -6

Question 2)

The profit function is given by:

We are asked to find the point where the company break even i.e. there is no profit or loss i.e. the possible value of x such that P(x)=0

i.e.

i.e.

( As the square of a number can't be negative.

Hence, is not a solution)

Hence, the solution is:

The correct answer is:

      D.  4 years    

Question 3)

The polynomial function is given by:

We know that the number of sign changes of function f(x) gives the possible number of positive real roots

and  the number of sign changes of function f(-x) gives the possible number of negative real roots.

The number of sign changes in f(x) is 1

(Hence, f(x) has at most 1 positive real root)

and

The number of sign changes in f(x) is 3

(Hence, f(x) has at most 3 negative real root)

              The correct answer is:

                 C.      3 or 1

step-by-step explanation: