how many real zeros does the following quadratic function have?

\f(x) = 5x^2 + 10x + 5\

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

no real zeros

two real zeros

Question

how many real zeros does the following quadratic function have?

\f(x) = 5x^2 + 10x + 5\

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

no real zeros

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": [ "Quadratic Functions", "Number of Quadratic Solutions" ], "new_concepts": [], "current_concepts": [ "Quadratic Functions", "Number of Quadratic Solutions", "Quadratic Zeros" ] } ## Identify the coefficients Using the **Quadratic Functions** knowledge point $$ \begin{aligned} &f(x) = 5x^2 + 10x + 5\ &a = 5,\quad b = 10,\quad c = 5 \end{aligned} $$ ## Calculate the discriminant Using the **Number of Quadratic Solutions** knowledge point $$ \begin{aligned} &D = b^2 - 4ac\ &D = 10^2 - 4(5)(5) = 100 - 100 = 0 \end{aligned} $$ ## Determine the number of real zeros Using the **Number of Quadratic Solutions** knowledge point $$ \begin{aligned} &D = 0 \implies \text{Exactly one real zero} \end{aligned} $$

no real zeros

two real zeros

one real zero

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Number of Quadratic Solutions" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the coefficients

Calculate the discriminant

Determine the number of real zeros

Answer: