Final answer:
The discriminant determines the number of real solutions in a quadratic equation. For the equation 2x² + bx + 5 = 0, b must be greater than or equal to √40 or less than or equal to -√40 to have real solutions.
Step-by-step explanation:
The discriminant in a quadratic equation of the form ax² + bx + c = 0 determines the nature and number of solutions. The discriminant is found using the formula b² - 4ac. If the discriminant is positive, there are two distinct real solutions; if it is zero, there's exactly one real solution (a repeated root); and if it's negative, there are no real solutions, only two complex solutions.
To find the values of b such that 2x² + bx + 5 = 0 has real solutions, we set the discriminant greater than or equal to zero, which gives us b² - 4(2)(5) ≥ 0, simplifying to b² ≥ 40. Hence, b must be greater than or equal to √40 or less than or equal to -√40.