Which of the following describes the roots of the polynomial function f(x) = (x-3)^4 (x + 6) squared?
–3 with multiplicity 2 and 6 with multiplicity 4
–3 with multiplicity 4 and 6 with multiplicity 2
3 with multiplicity 2 and –6 with multiplicity 4
3 with multiplicity 4 and –6 with multiplicity 2

Option d: 3 with multiplicity 4 and –6 with multiplicity 2

Explanation:

The function is

To determine the roots of a polynomial, let us substitute in the function

Thus, we have,

Thus, we have,

First solving the expression , we have,

with multiplicity 4.

Also, solving the expression , we have,

with multiplicity 2.

Thus, the roots of the polynomial function is 3 with multiplicity 4 and –6 with multiplicity 2

Hence, Option d is the correct answer.

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.