un nuevo diseño para un juego de diversiones consiste en hacer girar a una velocidad constante una circunferencia dentro de la cual estan ubicadas varias canastas con personas alrededor de un triángulo equilátero de lado x, si el de la rueda es 0.5 unidades, la cantidad de vueltas dadas por la rueda para recorrer todo el triángulo será: A. 5 B. 3 C. 6 D. # (π)

the bolded word " farsighted" could be replaced with visionary.

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.