To determine when the equation ax^2 + bx + c = 0 has equal roots, we need to consider the given equation b = ac and analyze the coefficients a, b, and c.

1. Understanding the equation b = ac:
- This equation implies that b is equal to the product of a and c.
- It can also be rewritten as ac - b = 0.

2. The discriminant of the quadratic equation:
- The discriminant is the expression inside the square root in the quadratic formula, which helps determine the nature of the roots.
- The discriminant is given by D = b^2 - 4ac.

3. Conditions for equal roots:
- For the quadratic equation to have equal roots, the discriminant D must be equal to zero.
- This is because when D = 0, the square root becomes zero, resulting in only one solution.

4. Substituting the value of b from the given equation:
- We substitute b = ac into the discriminant to determine the condition for equal roots.
- D = (ac)^2 - 4ac = a^2c^2 - 4ac = ac(ac - 4).

5. Analyzing the conditions for equal roots:
- For the discriminant to be zero, we need ac(ac - 4) = 0.
- This equation is satisfied if either ac = 0 or ac - 4 = 0.

6. Solving the equations:
- If ac = 0, then either a = 0 or c = 0.
- If ac - 4 = 0, then ac = 4, which implies a = 4/c.

7. Conclusion:
- The equation ax^2 + bx + c = 0 has equal roots if:
a) a = 0 or c = 0 (ac = 0)
b) a = 4/c (ac = 4)

Therefore, the correct answer is option 'B': a = c. This means that the equation will have equal roots if the coefficients a and c are equal.