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 ?
Since we are using 3 six-sided die to compute A, B and C values for a quadratic equation AX2 + BX + C = 0, there are 6 cubed, or 216, unique combinations. In order for the equation to have real roots, B squared - 4 x A x C must be greater than or equal to zero. A straight-forward Excel model shows this occurs 43 out of 216 times. The probability of realizing rational roots is therefore 43/216 = 19.9%. Gordon S.
Roots of Quadratic Equation
