Final answer:
Zeros of the quadratic polynomial p(x)=(k-2)x²-4x+k can be found using the quadratic formula, substituting a = k-2, b = -4, and c = k, then solving for x, ensuring k is not 2 to avoid division by zero.
Step-by-step explanation:
To find the zeros of the quadratic polynomial p(x) = (k-2)x² - 4x + k, where k is the value of the constant, we can use the quadratic formula which is:
x = −b ± √(b² - 4ac) / (2a)
In our polynomial, a = k-2, b = -4, and c = k. Plugging these values into the quadratic formula gives us:
x = (4 ± √((-4)² - 4(k - 2)k)) / (2(k - 2))
x = (4 ± √(16 - 4k² + 8k)) / (2k - 4)
Simplify under the square root and calculate for potential values of k when k does not make the denominator zero, which is when k is not 2.