Question

one solution to a quadratic function, f, is given below.\\(\sqrt{7} + 5i\\)\
which of the following statements is true about the given function?\
\\(\bigcirc\\) a. the other solution to function f is \\(\sqrt{7} - 5i\\).\
\\(\bigcirc\\) b. the other solution to function f is \\(-\sqrt{7} + 5i\\).\
\\(\bigcirc\\) c. function f has no other solutions.\
\\(\bigcirc\\) d. the other solution to function f is \\(-\sqrt{7} - 5i\\).

Explanation:

Step1: Recall complex conjugate root theorem

For quadratic functions with real coefficients, complex roots occur in conjugate pairs: if $a+bi$ is a root, then $a-bi$ is also a root.

Step2: Identify conjugate of given root

Given root: $\sqrt{7}+5i$. Its conjugate is $\sqrt{7}-5i$.

Step3: Match with options

The conjugate matches option A.

Answer:

A. The other solution to function $f$ is $\sqrt{7} - 5i$.