If the zeros of the quadratic polynomial ax^2+bx+c,c≠0 are equal, then

The zeroes of the quadratic polynomial are equal when the discriminant is equal to 0.

⇒ D = 0

⇒ b² – 4ac = 0

⇒ b² = 4ac

⇒ac = b²/4 >0 (I.e., the square of any positive or negative number is positive only)

⇒ ac > 0

Therefore, for ac > 0, a and c should have the same sign.