64sqrt 7 is a root of f(x) = x^2 - 28,672. Find the other roots of f(x). Write your answer as a list of simplified values separated by commas, if there is more than one value. ______

Identify Root Relationship: Since 64sqrt(7) is a root, the other root will be its opposite because the sum of the roots of a quadratic equation ax^2 + bx + c = 0 is -b/a. In this case, a = 1 and b = 0, so the sum of the roots is 0.Determine Other Root: The other root is -64sqrt(7) because 64sqrt(7) + (-64sqrt(7)) = 0.List All Roots: List the roots: 64sqrt(7), -64sqrt(7).

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$64\sqrt{7}$ is a root of $f(x) = x^2 - 28,672$ . 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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Math Problems

Precalculus

Conjugate root theorems

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64\sqrt{7}

is a root of

f(x) = x^2 - 28,672

. 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

Identify Root Relationship: Since $64\sqrt{7}$ is a root, the other root will be its opposite because the sum of the roots of a quadratic equation $ax^2 + bx + c = 0$ is $-b/a$ . In this case, $a = 1$ and $b = 0$ , so the sum of the roots is $0$ .
Determine Other Root: The other root is $-64\sqrt{7}$ because $64\sqrt{7} + (-64\sqrt{7}) = 0$ .
List All Roots: List the roots: $64\sqrt{7}$ , $-64\sqrt{7}$ .