Question Find the true statements about the polynomial $f(x) = x^{2} - 12x + 36$. Options: A) Two distinct linear factors, B) Roots at $x = \pm 6$, C) At least one complex root, D) Satisfies Fundamental Theorem of Algebra.

Studdy Solution
Determine the truth of statement D: The polynomial which defines $f(x)$ satisfies the Fundamental Theorem of Algebra.
Since $f(x)$ has exactly 2 roots (both are $x = 6$), it satisfies the Fundamental Theorem of Algebra. Therefore, statement D is true.
The true statements about $f(x) = x^2 - 12x + 36$ are:
D The polynomial which defines $f(x)$ satisfies the Fundamental Theorem of Algebra.