Determine the number and type of solutions of the given quadratic equation. Do not solve. 
$-4x^2+4x+5=0$

• A. 2 real solutions 
• B. 1 real solution 
• C. 2 imaginary solutions 

Answer: (A)

Verified step by step guidance

1. Identify the standard form of a quadratic equation, which is ax^2 + bx + c = 0. In this case, the equation is -4x^2 + 4x + 5 = 0, where a = -4, b = 4, and c = 5.
2. To determine the number and type of solutions, calculate the discriminant using the formula: D = b^2 - 4ac.
3. Substitute the values of a, b, and c into the discriminant formula: D = (4)^2 - 4(-4)(5).
4. Simplify the expression to find the value of the discriminant.
5. Interpret the discriminant: If D > 0, there are 2 real solutions; if D = 0, there is 1 real solution; if D < 0, there are 2 imaginary solutions.