Find the zero (s) of this function: y=x^2-17x+52

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}.

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