I assume that should read:y = (x-8)(x+3)^2
(where the "^" stands for power)
Since the polynomial is already factored, it is clear that it has the roots 8, -3, and -3; in other words, three roots (including one double root); or two, if you count the duplicates only once.
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The browser used for posting question is rubbish and most mathematical symbols are rejected. Howeer, if the function isy = (x - 8)*(x + 3)^2 then there are two distinct roots: one single and one double.