Final answer:
To find the solutions of the equations, we calculate the discriminant, which determines the number of real solutions. Equation B and C have one solution, equation D has two solutions, and equation A has no real solutions.
Step-by-step explanation:
To determine which of the given equations have one solution, two solutions, or no real solutions, we need to determine the discriminant of each equation. The discriminant is given by the formula:
discriminant = b^2 - 4ac
If the discriminant is greater than zero, the equation has two real solutions. If the discriminant is equal to zero, the equation has one real solution. If the discriminant is less than zero, the equation has no real solutions. Let's calculate the discriminants for each equation:
A. Discriminant = (-4)^2 - 4(1)(5) = -4 < 0 No real solutions.
B. Discriminant = (-4)^2 - 4(1)(4) = 0 One real solution.
C. Discriminant = (-4)^2 - 4(1)(16) = 0 One real solution.
D. Discriminant = (-4)^2 - 4(1)(25) = 24 > 0 Two real solutions.
Therefore, equation B and C have one real solution, equation D has two real solutions, and equation A has no real solutions.