Which situation results in a final value of zero? A the overall change in temperature when the temperature goes from –10°F to 10°F
B the total profit made when a person buys an item for $2.25 and then sells the item for $2.25
the overall change in altitude of a hot air balloon after rising 21 kilometers from sea level
D the total distance a person travels when he bikes 3.1 miles to school and then bikes 3.1 miles back home

step-by-step explanation:

i found the koficent of the linear function and i foun c acordind to the strict formula y=kx+c and then i took 2 as an x and replacet it on the formula i found and then foun the y

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.

answer: (x+2) (x+3) are the binomials for your question : )

~dasgupta/mathbook/append17dec2k8.pdf