Difference between revisions of "2020 AIME II Problems/Problem 11"
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| − | + | ==Problem== | |
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| + | Let <math>P(X) = x^2 - 3x - 7</math>, and let <math>Q(x)</math> and <math>R(x)</math> be two quadratic polynomials also with the coefficient of <math>x^2</math> equal to <math>1</math>. David computes each of the three sums <math>P + Q</math>, <math>P + R</math>, and <math>Q + R</math> and is surprised to find that each pair of these sums has a common root, and these three common roots are distinct. If <math>Q(0) = 2</math>, then <math>R(0) = \fracmn</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m + n</math>. | ||
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| + | ==Solution== | ||
| + | ==Video Solution== | ||
| + | https://youtu.be/BQlab3vjjxw ~ CNCM | ||
| + | ==See Also== | ||
Revision as of 18:10, 7 June 2020
Contents
Problem
Let 
, and let 
and 
be two quadratic polynomials also with the coefficient of 
equal to 
. David computes each of the three sums 
, 
, and 
and is surprised to find that each pair of these sums has a common root, and these three common roots are distinct. If 
, then $R(0) = \fracmn$ (Error compiling LaTeX. Unknown error_msg), where 
and 
are relatively prime positive integers. Find 
.
Solution
Video Solution
https://youtu.be/BQlab3vjjxw ~ CNCM
