In the Land of Clinkets, the local Winkets and Flinkets earn their wealth in stars, crescents, and nuggets. Every
5 stars equals the value of 1 crescent. Every 5 crescents
are worth 1 nugget.
• Chief Winket has 250 nuggets, 50 stars, and 200
crescents.
• His counterpart, Chief Flinket, has twice as many
crescents. 3 times as many stars, but just 200
nuggets.
A new Blinket costs 600 nuggets.
If they combine their wealth, how many more stars must
they earn in order to have enough stars to each buy a
new Blinket?

the line of

9x

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.