Which answer best describes the complex zeros of the polynomial function? f(x)=x3−x2+6x−6 the function has two real zeros and one nonreal zero. the graph of the function intersects the x-axis at exactly one location. the function has one real zero and two nonreal zeros. the graph of the function intersects the x-axis at exactly one location. the function has one real zero and two nonreal zeros. the graph of the function intersects the x-axis at exactly two locations. the function has three real zeros. the graph of the function intersects the x-axis at exactly three locations.

The correct option is 2.

Explanation:

The given polynomial is,

By rational root theorem 1 and -1 are possible roots of all polynomials.

put x=1

Since the value of f(x) is 0 at x=1. So 1 is a real root of the polynomial.

Divide the given polynomial by  (x-1) using synthetic division method.

Equate each factor equal to 0.

So, the given polynomial have one real root and 2 non real roots. Since the function have one real root therefore the function intersects the x-axis at exactly one location.

Thus, the correct option is 2.

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step-by-step explanation: