# Finding the probability that the roots of a quadratic exist.

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You assign uniform distributions to a, b, and c (each between 0 and 1). What is your probability that all the roots of the following equation are real? So, if you used the quadratic formula to solve the equation and you got the square root of a negative number as a root then the roots would not be real.

ax^2 + bx + c = 0

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#### Solution Preview

Since a, b and c are random variables following uniform distribution on the interval (0,1), the distribution functions are the same as F(x)=x, 0<x<1; F(x)=1, ...

#### Solution Summary

In the response below the author first finds the probability that the roots of a quadratic exist then discusses the nature of solving such a question.

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