If the zeroes of the quadratic polynomial ax^2 + bx + c, c ≠ 0 are equal, then
A. c and a have opposite signs
B. c and b have opposite signs
C. c and a have the same sign
D. c and b have the same sign

To solve this, we need to analyze the condition for a quadratic polynomial to have equal zeroes. The given polynomial is:

a(x^2) + bx + c, where c ≠ 0.

For the zeroes of a quadratic polynomial to be equal, the discriminant must be zero. The discriminant (Δ) of a quadratic equation ax^2 + bx + c = 0 is given by:

Δ = b² - 4ac.

For the roots to be equal, the discriminant must be zero. Therefore:

b² - 4ac = 0.

This implies:

b² = 4ac.

Now, let's analyze the relationship between a, b, and c. We are given that c ≠ 0, and we are looking for the correct statement about the signs of a, b, and c.

From b² = 4ac, we can deduce that the product of a and c must be positive, because b² is always non-negative. So, for b² to equal 4ac, a and c must have the same sign (both positive or both negative).

Thus, the correct answer is:

C. c and a have the same sign.