select the correct answer.

a solution to a quadratic function, $f$, is given below.

$-3 - 5i$

which statement is true about the given function?

- the other solution to function $f$ is $-3 + 5i$.
- the other solution to function $f$ is $3 - 5i$.
- the other solution to function $f$ is $3 + 5i$.
- function $f$ has no other solutions.

Question

select the correct answer.

a solution to a quadratic function, $f$, is given below.

$-3 - 5i$

which statement is true about the given function?

- the other solution to function $f$ is $-3 + 5i$.
- the other solution to function $f$ is $3 - 5i$.
- the other solution to function $f$ is $3 + 5i$.
- function $f$ has no other solutions.

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 Conjugate Theorem" ] } ## Apply the Complex Conjugate Root Theorem $$ \begin{aligned} &\text{Given solution: } z_1 = -3 - 5i \ &\text{For a quadratic function with real coefficients, complex roots must occur in conjugate pairs.} \ &\text{Conjugate of } a + bi \text{ is } a - bi \ &z_2 = \overline{z_1} = -3 + 5i \end{aligned} $$

(A) The other solution to function $f$ is $-3 + 5i$.

(B) The other solution to function $f$ is $3 - 5i$.

(C) The other solution to function $f$ is $3 + 5i$.

(D) Function $f$ has no other solutions.

{ "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

Answer: