how many real zeros does the following quadratic function have?

\f(x) = 9x^2 + 6x + 1\

remember the quadratic formula: \x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\

two real zeros
no real zeros
one real zero

Question

how many real zeros does the following quadratic function have?

\f(x) = 9x^2 + 6x + 1\

remember the quadratic formula: \x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\

two real zeros
no real zeros
one real zero

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Discriminant Analysis", "Number of Quadratic Solutions" ], "new_concepts": [], "current_concepts": [ "Discriminant Analysis", "Number of Quadratic Solutions", "Quadratic Zeros" ] } ## Identify coefficients Using the **Discriminant Analysis** knowledge point $$ \begin{aligned} &f(x) = 9x^2 + 6x + 1\ &a = 9,\quad b = 6,\quad c = 1 \end{aligned} $$ ## Calculate discriminant Using the **Discriminant Analysis** knowledge point $$ \begin{aligned} &D = b^2 - 4ac\ &D = 6^2 - 4(9)(1) = 36 - 36 = 0 \end{aligned} $$ ## Determine number of zeros Using the **Number of Quadratic Solutions** knowledge point $$ \begin{aligned} &D = 0 \implies \text{exactly one real zero} \end{aligned} $$

two real zeros

no real zeros

one real zero

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Discriminant Analysis" ] }

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QUESTION IMAGE

Question

Explanation:

Identify coefficients

Calculate discriminant

Determine number of zeros

Answer: