How many zeroes can the polynomial f(x) = (x−2)² + 4 have?

Given polynomial is f(x) = (x−2)² + 4.

We know that to find the zeroes of a polynomial, we need to equate it to zero.

Therefore, f(x) = 0

⇒ (x−2)² + 4 = 0

⇒ (x−2)² = −4

Here, we cannot find 'x' because the square of a real number cannot be negative.

Therefore, the given polynomial doesn't have a zero.