2023 AMC 12B Problems/Problem 6
Solution 1
Looking at the polynomial, we can use Vieta's formulas. Let's say the roots are r, s, and t. Then We know that r, s, and t are integers, so we can list the possibilities for distinct solutions using the third formula. We find that can be and . Remember that r, s, and t have to be different. That's 5 solutions. We can also use those values to find the values of a and b to check that none of them are distinct, and we'll find that they are and . This means that there are