Juan borrows a total of $95,500 to pay for medical school. He borrows part of the money from the school whereby he will pay 4.6% simple interest. He borrows the rest of the money through a government grant that will charge him 6.2% interest. In both cases, he is not required to pay off the principal or interest during
his 2 years of medical school. However, at the end of 2 years, he will owe a total of $9858 for the interest from both loans. How much did he borrow from each
source?

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.

show us the triangle so we can answer it