Answer by Felix Marin for Probability that a quadratic equation has real roots
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View ArticleAnswer by K. Miller for Probability that a quadratic equation has real roots
We know from the quadratic formula that the polynomial $Ax^2 + Bx + C$ has real roots if $B^2 - 4AC \geq 0$. We can think of this problem in terms of volumes. To do so, it's easier if we rename the...
View ArticleAnswer by Nick Peterson for Probability that a quadratic equation has real roots
I would probably start by breaking into cases based on $A$ and $C$.Conditioned on $A$ and $C$ having different signs, there are always real roots (because $4AC\leq 0$, so that $B^2-4AC\geq0$). The...
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Probability that a quadratic equation has real roots
ProblemThe premise is almost the same as in this question. I'll restate for convenience.Let $A$, $B$, $C$ be independent random variables uniformly distributed between $(-1,+1)$. What is the...
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