what are the possible numbers of positive, negative, and complex zeros of f(x) = −3x4 −
5x3 − x2 − 8x + 4?
select one:
a. positive: 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0
b. positive: 1; negative: 3 or 1; complex: 2 or 0
c. positive: 3 or 1; negative: 1; complex: 2 or 0
d. positive: 4 or 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0

b.

Step-by-step explanation:

We have to look at sign changes in f(x) to determine the possible positive real roots.

There is only one sign change here, between the -8x and the +4.  So that means there is only 1 possible real positive root.

Now we have to look at sign changes in f(-x) to determine the possible negative real roots.

There are 3 sign changes here.  That means there are either 3 negative roots or 3-2 = 1 negative root.  So we have:

1 positive

3 or 1 negative

We need to pair them up now with all the possible combinations.

If we have 1 positive and 1 negative, we have to have 2 imaginary

If we have 1 positive and 3 negative, we have to have 0 imaginary

Keep in mind that the total number or roots--positive, negative, imaginary--have to add up to equal the degree of the polynomial.  This is a 4th degree polynomial, so we will have 4 roots.

answer is d-29

step-by-step explanation:

since you didn't include the picture, i can give you the description so you know how to pick the correct answer. the third quartile of a data is always shown in a box plot. in the middle of your graph should be a box. the third quartile is the value that goes with the far right edge of the box.

24

step-by-step explanation: