2020 AIME II Problems/Problem 11

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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 $R(0) = \fracmn$ (Error compiling LaTeX. Unknown error_msg), where $m$ and $n$ are relatively prime positive integers. Find $m + n$.

Solution

Video Solution

https://youtu.be/BQlab3vjjxw ~ CNCM

See Also