Final answer:
Using the discriminant, which is 89 for the quadratic equation 2x² + 5x - 8 = 0, we can conclude there are two real and distinct solutions because the discriminant is positive and non-zero. Option b is the correct answer.
Step-by-step explanation:
We can determine the number and type of solutions of the quadratic equation 2x² + 5x - 8 = 0 using the discriminant. The discriminant is part of the quadratic formula, which is used to find the roots/solutions of a quadratic equation in the form ax² + bx + c = 0. The discriminant is b² - 4ac.
For our equation, a = 2, b = 5, and c = -8. Plugging these into the discriminant gives us:
Discriminant = b² - 4ac = (5)² - 4(2)(-8) = 25 + 64 = 89
Because the discriminant is positive and not zero, we know there are two real and distinct solutions for the equation 2x² + 5x - 8 = 0. If the discriminant were zero, there would be one real and repeated solution. Had it been negative, there would be no real solutions, only complex ones.