Advanced Math/statistics

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Expert: Sherry Wallin - 2/2/2011


Question
The values of a,b,c in a quadratic a x2 + b x + c = 0 is determined by throwing an
ordinary die with face values 1,2,3,4,5,6. Find the probability of getting real roots
of the quadratic.

Answer

real roots for quadrat
Neal~

In order to find the probability that you will get real roots in the quadratic ax^2 + bx + c = 0 you need to determine how many possibilities there are for the coefficients a,b, and c. There are 6 ways to throw for the coefficient a and 6 ways to throw for the coefficient b as well as 6 ways to throw for the coefficient c, for a grand total of 6^3 = 216 ways to select the coefficients for a,b, and c.

In order for a quadratic to have real roots the discriminant must be greater than or equal to zero, i.e. b^2-4ac >=0 which implies that b^2>=4ac.

Please see the attached table of values. I have shown all the possible combinations for 4ac.

Then you need to determine how many of the possibilities have the characteristic that b^2-4ac >= 0 which implies b^2 >=4ac or
(4ac <= b^2), thus take each of the possible products of ac and multiple them by 4 and find out how many are less than or equal to each of the b^2's, i.e. 1^1 = 1, 2^2 = 4, 3^ = 9, 4^2 = 16, 5^2 = 25, and 6^2 = 36. The sum of those products over the 216 possible events will give you your answer!

Math Prof

Sherry Wallin

Expertise

I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

Experience

I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

Education/Credentials
I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

Awards and Honors
Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0

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