If a polynomial function f(x) has roots –8, 1, and 6i, what must also be a root of f(x)?

–6

–6i

6 – i

6

For any polynomial with a complex root, the imaginary part of the complex root always has positive and negaive component. Since one of the roots of this polynomial is 6i, then -6i must also be a root of the function.

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jainveenamrata jainveenamrata · Answer 2 · 2022-07-04T07:23:36+02:00

The fourth root of the polynomial will be –6i. Then the correct option is B.

What are the roots of the polynomial?

The polynomial is given below.

[tex]\rm f(x) = a_0x^n + a_1 x^{n - 1}+ ....+ a_{n-2}x^2 + a_{n-1}x + a_nx^0[/tex]

The roots of the polynomial are equal to n or less than n.

And if one imaginary root is a + bi, then the other imaginary root will be a – bi.

If a polynomial function f(x) has roots –8, 1, and 6i.

Then the fourth root of the polynomial will be –6i.

Then the correct option is B.

More about the roots of the polynomial link is given below.

https://brainly.com/question/1514617

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If a polynomial function f(x) has roots –8, 1, and 6i, what must also be a root of f(x)? –6 –6i 6 – i 6

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What are the roots of the polynomial?

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If a polynomial function f(x) has roots –8, 1, and 6i, what must also be a root of f(x)?

–6

–6i

6 – i

6