Final answer:
To find a pair of values for a and c such that -4x c=-ax^2 has two imaginary solutions, choose a positive value for c and a negative value for a.
Step-by-step explanation:
To find a pair of values for a and c such that -4x c=-ax^2 has two imaginary solutions, we need to ensure that the discriminant of the quadratic equation is negative. The discriminant is the expression inside the square root of the quadratic formula: b^2 - 4ac. In this case, we have -4c = -a and we know that a is positive. So, to make the discriminant negative, we can choose a positive value for c and a negative value for a.
For example, let's say a = -2 and c = 3. Substituting these values into the equation, we get -4x (3) = -(-2)x^2, which simplifies to -12x = 2x^2. By rearranging the equation, we get 2x^2 + 12x = 0. The discriminant in this case is b^2 - 4ac = 12^2 - 4(2)(0) = 144, which is positive. Therefore, this pair of values for a and c does not result in two imaginary solutions.