You receive a gift card for trading cards from a local store. the function d=20-1.95c represents the remaining dollars d on the gift card after obtaining c packages of cards. find the zero of this function. describe what this value means in this context.

The zero of this function is 10.2564103 ( or 10 if you round it) because you need to substitute d with 0. The value of this context means the maximum amount of trading cards you can get with the gifts card

1,8,15,22,29,36,43,50

step-by-step explanation:

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.