Final answer:
A quadratic equation can have either two, one, or no real solutions. In the given equation, 2x² + 2x – 1 = 0, it has two real solutions.
Step-by-step explanation:
A quadratic equation of the form ax² + bx + c = 0 can have either two, one, or no real solutions. To determine the number of solutions, we can use the discriminant, which is the expression b² - 4ac. If the discriminant is greater than 0, the equation has two real solutions. If the discriminant is equal to 0, the equation has one real solution. If the discriminant is less than 0, the equation has no real solutions.
In the given equation 2x² + 2x – 1 = 0, a = 2, b = 2, and c = -1. Plugging these values into the discriminant formula, we get:
Discriminant = (2)² - 4(2)(-1) = 4 + 8 = 12
Since the discriminant is greater than 0, the quadratic equation has two real solutions.