October 02, 2011

11. Quadractic Quizzicality

11. Quadractic Quizzicality

Question: Suppose B and C are random numbers from a uniform(0,1) distribution. What is the probabilty that x^2 + Bx + C = 0 has two real roots?

Solution: x has two real roots if its discriminant is greater than zero. i.e B^2 - 4C > 0.

So B^2 > 4C or c < B^2/4.

The sample space for B and C has an area of 1 and the area beneath the curve of C = B^2/4 represents the values for B and C that result in real roots.

So the probabilty that B^2 - 4C > 0 (the equation x^2 + Bx + C = 0 has two real roots) is the integral from 0 to 1 of B^2 /4 which is 1/12.


- One comment Not publicly viewable

  1. Jennifer Ingram

    what about extending this? Would it work for cubics? what about a different distribution?

    25 Oct 2011, 17:39


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