Printable

2019 AMC 10A Problem 24

Include the solution Back to the problem

2019 AMC 10A Problem 24AMC 10 Step by Step

Name: Date: September 13, 2026

Polynomials · difficulty 5 of 5 · about 7 min · position P21-25

Let $p$ , $q$ , and $r$ be the distinct roots of the polynomial $x^3 - 22x^2 + 80x - 67$ . It is given that there exist real numbers $A$ , $B$ , and $C$ such that $\dfrac{1}{s^3 - 22s^2 + 80s - 67} = \dfrac{A}{s-p} + \dfrac{B}{s-q} + \frac{C}{s-r}$ for all $s\not\in\{p,q,r\}$ . What is $\tfrac1A+\tfrac1B+\tfrac1C$ ?

A)
$243$
B)
$244$
C)
$245$
D)
$246$
E)
$247$

2019 AMC 10A Problem 24

Working