Let A, B, and C be independent random variables, uniformly distributed over [0,2], [0,1], and [0,10] respectively. What is the probability that both roots of the equation Ax2+Bx+C=0 are real?
Added by Carmen P.
Step 1
The roots of a quadratic equation are real if the discriminant is non-negative. The discriminant \( D \) for the equation \( Ax^2 + Bx + C = 0 \) is given by: \[ D = B^2 - 4AC \] We need to find the probability that \( D \geq 0 \). Show more…
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