2020 AIME II Problems/Problem 11

Problem

Let $P(X) = x^2 - 3x - 7$ , and let $Q(x)$ and $R(x)$ be two quadratic polynomials also with the coefficient of $x^2$ equal to $1$ . David computes each of the three sums $P + Q$ , $P + R$ , and $Q + R$ and is surprised to find that each pair of these sums has a common root, and these three common roots are distinct. If $Q(0) = 2$ , then $R(0) = \frac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m + n$ .

Solution

Video Solution

https://youtu.be/BQlab3vjjxw ~ CNCM

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2020 AIME II Problems/Problem 11

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Problem

Solution

Video Solution

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