Difference between revisions of "2021 Fall AMC 10A Problems/Problem 20"

Latest revision as of 01:28, 26 November 2021

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-== Problem ==
+#REDIRECT [[2021_Fall_AMC_12A_Problems/Problem_17]]
-How many ordered pairs of positive integers <math>(b,c)</math> exist where both <math>x^2+bx+c=0</math> and <math>x^2+cx+b=0</math> do not have distinct, real solutions?
-<math>\textbf{(A) } 4 \qquad \textbf{(B) } 6 \qquad \textbf{(C) } 8 \qquad \textbf{(D) } 10 \qquad \textbf{(E) } 12 \qquad</math>
-== Solution ==
-A quadratic equation has no real solutions if and only if the discriminant is nonpositive. Therefore: