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Flauer [41]
3 years ago
13

Which answer best describes the complex zeros of the polynomial function?

Mathematics
1 answer:
marysya [2.9K]3 years ago
3 0

<u>Answer-</u>

<em>D. The function has one real zero and two nonreal zeros. The graph of the function intersects the x-axis at exactly one location.</em>

<u>Solution-</u>

The given polynomial is,

f(x)=x^3-x^2+6x-6

The zeros of the polynomials are,

\Rightarrow f(x)=0

\Rightarrow x^3-x^2+6x-6=0

\Rightarrow x^2(x-1)+6(x-1)=0

\Rightarrow (x^2+6)(x-1)=0

\Rightarrow (x^2+6)=0,(x-1)=0

\Rightarrow x=\sqrt{-6},\ x=1

\Rightarrow x=1,\ \pm \sqrt6i

Therefore, this function has only one real zero i.e 1 and two nonreal zeros i.e ±√6i . The graph of the function intersects the x-axis at exactly one location i.e at x = 1

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