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Roots Of The Equation (Posted on 2003-08-20) Difficulty: 3 of 5
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 ?

See The Solution Submitted by Ravi Raja    
Rating: 2.6667 (9 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: solution | Comment 3 of 16 |
(In reply to solution by derek)

A program for doing this is:
DEFDBL A-Z
FOR a = 1 TO 6
 FOR b = 1 TO 6
   FOR c = 1 TO 6
    IF b * b > 4 * a * c THEN
      ct = ct + 1
    ELSEIF b * b = 4 * a * c THEN
      ct2 = ct2 + 1
    END IF
   NEXT
 NEXT
NEXT
PRINT USING "##.########"; ct / (6 * 6 * 6); ct2 / (6 * 6 * 6); ct / (6 * 6 * 6) + ct2 / (6 * 6 * 6)

which counts separately the cases where there are two distinct real roots from those cases where there is a double root. The results come out:

0.17592593 0.02314815 0.19907407
so the 19.9% probability of real roots is broken down into a 17.6% probability of two distinct real roots and 2.3% probability of a double real root.

  Posted by Charlie on 2003-08-20 10:19:30

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