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$-66\sqrt{5}$ is a root of $f(x) = x^2 - 21,780$ . 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.

-66\sqrt{5}

is a root of

f(x) = x^2 - 21,780

. 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.

Identify Opposite Root: Since $-66\sqrt{5}$ is a root, the other root will also be the negative of it because the sum of the roots of a quadratic equation $ax^2 + bx + c = 0$ is $-b/a$ . In this case, $b = 0$ , so the roots are opposites.
List Other Root: The other root is $66\sqrt{5}$ . Now we list both roots.
Final Polynomial Roots: The roots of the polynomial are $-66\sqrt{5}$ and $66\sqrt{5}$ .

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