Math Forum / Mathematics / Undergraduate Math / May 2005

Dear Rodrigo,

Roots of trinom are real when discriminant >= 0
or B^2-4*A*C >= 0
You have to compute Prob(B^2-4*A*C >= 0) A,B,C
uniform on interval [0,1] ,
you may experiment the case with a uniform random func. :
 (Rand1)^2-4*Rand2*Rand3 =  , indices means castings
  must be different ;follow the signs and values (to
  estimate the mean );
to go further : study the Law of B^2 and A*C ,

Courage,Alain.

Consider the horizontal a-c plane and the b-axis to be vertical. You need to calculate the volume of the solid above the surface b^2 = 4*a*c and below the plane b = 1.

I tried doing a double integral of the cross sectional area parallel to the a-c plane (in terms of a)  [c=1-(b^2/4) (1/a) from z^2 / 4 to 1
and then the height from 0 to 1 (in terms of b)  

and then took 1- the result
and got just over .2544 ...
Trying the same thing with several thousand simulations using Fathom software gives essentially the same answer...

Pat Ballew
Lakenheath UK

Thanks, everyone!

Weeks ago I was helpless about it and no one would answer it. I tried to solve using many ways and I finally found something before your answers pop up! I am amazing that people do care about PROBABILITY on this math forum. It seems there is no one specialized on it.

I have written a small .tex file on this matter and I would be glad to share it with anyone interested.

I thank you all for your right answers (at least I found the same results)...

Cheers,
Rodrigo