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$106$ is a root of $f(x) = x^2 + 11,236$ . 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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Complex conjugate theorem

Full solution

Q.

106

is a root of

f(x) = x^2 + 11,236

. 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.

Write as $x - 106$ : Since $106$ is a root, we can write it as $x - 106 = 0$ . Now we need to find the other root.
Find sum of roots: The sum of the roots of a quadratic equation $ax^2 + bx + c = 0$ is $-\frac{b}{a}$ . In our case, $a = 1$ and $b = 0$ , so the sum of the roots is $0$ .
Determine other root: If one root is $106$ , the other root must be $-106$ to sum up to $0$ .
Determine other root: If one root is $106$ , the other root must be $-106$ to sum up to $0$ .So the other root is $-106$ .

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