Let us consider the quadratic equation: ax˛ + bx + c = 0.
We assign values to the coefficients a, b and c by throwing a die.
What is the probability that the equation will have real roots ?
(In reply to
Full Solution by DJ)
One other point I should make:
If it is said that there must indeed be two distinct real roots (a single real root where b²=4ac is no longer valid), then the sets (a, b, c) corresponding to (1, 2, 1), (1, 4, 4), (2, 4, 2), (4, 4, 1), and (3, 6, 3) would not be valid.
This eliminates 5 of the original 43 valid sets, leaving 38, for an overall probability of 38/216(=19/108), which evaluates to 0.17592592592... .
The chance of having exactly one real root, incidentally, is 5/216=.023148148148... .
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Posted by DJ
on 2003-08-20 10:39:21 |
re: Full Solution
