Two Parabolas Common Tangent

1550AdeptCoordinate GeometryCombinatoricsAlgebra

AMC 12B · 2012 · Problem 13

Two parabolas have equations $y= x^2 + ax +b$ and $y= x^2 + cx +d$, where $a$, $b$, $c$, and $d$ are integers, each chosen independently by rolling a fair six-sided die. What is the probability that the parabolas will have at least one point in common?

Answer choices

\frac{1}{2}

\frac{25}{36}

\frac{5}{6}

\frac{31}{36}

0 students attempted0% solvedRating 1550

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