Final answer:
The quadratic equation 2x² - 3x - 8 = 0 has two real solutions because the discriminant, calculated as b² - 4ac, is positive (73 in this case).
Step-by-step explanation:
To determine the number of real solutions for the quadratic equation 2x² - 3x - 8 = 0, we can use the discriminant of the quadratic formula which is given by b² - 4ac. For this equation, a = 2, b = -3, and c = -8. Therefore, the discriminant is (-3)² - 4(2)(-8) = 9 + 64 = 73.
Since the discriminant is positive, this means that there are two real solutions to the equation. A positive discriminant always results in two real and distinct solutions, so the correct answer is B) Two real solutions.