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$52\sqrt{7}$ is a root of $f(x) = x^2 - 18,928$ . 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.

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Conjugate root theorems

Full solution

Q.

52\sqrt{7}

is a root of

f(x) = x^2 - 18,928

. 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.

Determine Opposite Root: Since $52\sqrt{7}$ is a root, the other root will also be its opposite because the sum of the roots is the coefficient of $x$ , which is $0$ in this case ( $x^2$ has no $x$ term).
Identify Other Root: The other root is $-52\sqrt{7}$ .
List All Roots: List the roots: $52\sqrt{7}$ , $-52\sqrt{7}$ .

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