Use the discriminant to determine the number of real solutions of x^2+14x+24=0.
blank real solution(s)
The discriminant of a quadratic equation of the form ax^2 + bx + c = 0 is given by the expression b^2 - 4ac.
In this case, a = 1, b = 14, and c = 24. Therefore, the discriminant is:
(14)^2 - 4(1)(24) = 196 - 96 = 100.
Since the discriminant is a positive number (100 > 0), this means that the quadratic equation has two distinct real solutions.