Agroup of n ? 4 people stand in line to purchase movie tickets. assume that there are r ? 2 men and s ? 2 women, such that r + s = n. you should not assume that the men and women are indistinguishable from each other.
a) how many possible lines are there such that, starting from the front of the line, there are exactly three points where the line alternates from man to woman, or woman to man? for example, if n = 6, r= 4, s = 2, then one line arrangement that should be counted is (man 1, man 2, woman 1, man 3, man 4, woman 2). note that there are exactly three points of alteration- between man 2 and woman 1, woman 1 and man 3, and man 4 and woman 2
b) solve the above problem with the added condition that man 2 must be the second man in line, woman 2 must be the second woman in line, or both

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!

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