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In any polynomial when you have an imaginary root, there is always another imaginary root that is the conjugate of the first one:
1st root:  4 + 17i
2nd root: 4 - 17i  (the conjugate of the 1st one)
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If a root is [tex]4 + i\, 17[/tex], then another root of the polynomial must be [tex]4 - i\,17[/tex].

Let suppose that given polynomial is a quadratic equation. According to the quadratic formula, there are two complex roots of the form [tex]\alpha + i\,\beta[/tex] and [tex]\alpha - i\,\beta[/tex]  when discriminant is less than zero.

If a root is [tex]4 + i\, 17[/tex], then another root of the polynomial must be [tex]4 - i\,17[/tex] according to the quadratic formula.

We kindly invite to check this question on quadratic formula: https://brainly.com/question/9300679

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