Answer:
The zeroes are {-4, 13}
Step-by-step explanation:
Your best bet here is to determine the zeros using the quadratic formula or "completing the square."
Completing the square,
y = x² - 17x +52, or
y = (x - 17/2)² - (17/2)² +52, or
y = (x - 17/2)² - 289/4 +208/4, or
y = (x - 17/2)² - 81/4
We set this = to 0, as we want the zeros. Then:
(x - 17/2)² - 81/4 = 0, or
x - 17/2 = ±9/2, after having taken the square root of both sides.
Thus, one root is x = 17/2 + 9/2, or 26/2, or 13, and the other is
x = 1/2 - 9/2, or -8/2, or -4.
The zeroes are {-4, 13}.
