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$62+58i$ is a root of $f(x) = x^2–124x+7208$ . Find the other roots of $f(x)$ .

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Complex conjugate theorem

Full solution

Q.

62+58i

is a root of

f(x) = x^2–124x+7208

. Find the other roots of

f(x)

.

Determine total number of roots: The number of roots of a polynomial is equal to its degree. We have: $\newline$ $f(x) = x^2 - 124x + 7208$ $\newline$ Determine the total number of roots. The degree of $f(x)$ is $2$ . So, the number of roots: $2$ .
Find other root: If $a + bi$ is a root, then its conjugate $a - bi$ is also a root of $f(x)$ . Given root: $62 + 58i$ $\newline$ Find the other root of $f(x) = x^2 – 124x + 7208$ . The conjugate of $62 + 58i$ is $62 - 58i$ . $\newline$ Since $f(x)$ has only $2$ roots, $62 - 58i$ is the only other root.

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