select the correct answer.

one solution of the quadratic function $f$ is $-5 - 7i$. which statement is true about this function?

another solution of function $f$ is $5 - 7i$.
another solution of function $f$ is $5 + 7i$.
function $f$ has no other solutions.
another solution of function $f$ is $-5 + 7i$.

Question

select the correct answer.

one solution of the quadratic function $f$ is $-5 - 7i$. which statement is true about this function?

another solution of function $f$ is $5 - 7i$.
another solution of function $f$ is $5 + 7i$.
function $f$ has no other solutions.
another solution of function $f$ is $-5 + 7i$.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Complex Roots" ], "new_concepts": [], "current_concepts": [ "Complex Roots", "Complex Conjugates" ] } ## Apply the Complex Conjugate Root Theorem $$ \begin{aligned} &\text{If } a + bi \text{ is a root of a quadratic function with real coefficients, then its complex conjugate } a - bi \text{ is also a root.}\ &\text{Given root: } z_1 = -5 - 7i \end{aligned} $$ ## Find the complex conjugate $$ \begin{aligned} &z_2 = \overline{z_1} = -5 + 7i \end{aligned} $$

Another solution of function $f$ is $5 - 7i$.

Another solution of function $f$ is $5 + 7i$.

Function $f$ has no other solutions.

Another solution of function $f$ is $-5 + 7i$.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Complex Roots" ] }

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QUESTION IMAGE

Question

Explanation:

Apply the Complex Conjugate Root Theorem

Find the complex conjugate

Answer: