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$-176$ is a root of $f(x) = x^2 + 30,976$ . Find the other roots of $f(x)$ . $\newline$ Write your answer as a list of simplified values separated by commas, if there is more than one value. $\newline$ ______ $\newline$

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Complex conjugate theorem

Full solution

Q.

-176

is a root of

f(x) = x^2 + 30,976

. Find the other roots of

f(x)

.

\newline

Write your answer as a list of simplified values separated by commas, if there is more than one value.

\newline

______

\newline

Degree of Function: $f(x) = x^2 + 30,976$ has a degree of $2$ , so it has $2$ roots.
Finding Roots: If $-176$ is a root, the other root is its opposite, $176$ , because the sum of the roots of a quadratic equation $ax^2 + bx + c = 0$ is $-b/a$ . Here, $b = 0$ , so the roots are opposites.
Identifying Other Root: The other root is $176$ .

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