how many real zeros does the following quadratic function have?

(f(x) = 16x^2 + 16x + 4)

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

no real zeros
one real zero
two real zeros

Question

how many real zeros does the following quadratic function have?

(f(x) = 16x^2 + 16x + 4)

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

no real zeros
one real zero
two real zeros

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 the coefficients Using the **Discriminant Analysis** knowledge point $$ \begin{aligned} &a = 16\ &b = 16\ &c = 4 \end{aligned} $$ ## Calculate the discriminant Using the **Discriminant Analysis** knowledge point $$ \begin{aligned} \Delta &= b^2 - 4ac\ &= 16^2 - 4(16)(4)\ &= 256 - 256\ &= 0 \end{aligned} $$ ## Determine the number of real zeros Using the **Number of Quadratic Solutions** knowledge point $$ \begin{aligned} &\Delta = 0 \implies \text{Exactly one real solution} \end{aligned} $$

no real zeros

one real zero

two real zeros

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

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QUESTION IMAGE

Question

Explanation:

Identify the coefficients

Calculate the discriminant

Determine the number of real zeros

Answer: