select the correct answer.

which statement best describes the zeros of the function (h(x) = (x + 9)(x^2 - 10x + 25))?

- the function has three complex zeros.
- the function has three distinct real zeros.
- the function has one real zero and two complex zeros.
- the function has two distinct real zeros.

Question

select the correct answer.

which statement best describes the zeros of the function (h(x) = (x + 9)(x^2 - 10x + 25))?

- the function has three complex zeros.
- the function has three distinct real zeros.
- the function has one real zero and two complex zeros.
- the function has two distinct real zeros.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Zeros and Factors", "Quadratic Functions" ], "new_concepts": [ "Multiplicity of Zeros" ], "current_concepts": [ "Zeros and Factors", "Quadratic Functions", "Multiplicity of Zeros" ] } ## Find the zeros of each factor $$ \begin{aligned} &x + 9 = 0 \implies x = -9 \ &x^2 - 10x + 25 = 0 \end{aligned} $$ ## Factor the quadratic expression $$ \begin{aligned} &x^2 - 10x + 25 = (x - 5)^2 \ &(x - 5)^2 = 0 \implies x = 5 \end{aligned} $$ ## Determine the number of distinct real zeros $$ \begin{aligned} &\text{Zeros: } x = -9 \text{ (multiplicity 1), } x = 5 \text{ (multiplicity 2)} \ &\text{Distinct real zeros: } \{-9, 5\} \implies 2 \text{ distinct real zeros} \end{aligned} $$

The function has three complex zeros.

The function has three distinct real zeros.

The function has one real zero and two complex zeros.

The function has two distinct real zeros.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Zeros and Factors" ] }

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QUESTION IMAGE

Question

Explanation:

Find the zeros of each factor

Factor the quadratic expression

Determine the number of distinct real zeros

Answer: