identify the nature of the quadratic equation $x^2 + 9x + 10 = 0$.

* real and equal
* real and distinct

Question

identify the nature of the quadratic equation $x^2 + 9x + 10 = 0$.

* real and equal
* real and distinct

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 of Quadratic", "Quadratic Equations" ], "new_concepts": [], "current_concepts": [ "Quadratic Equations", "Discriminant of Quadratic", "Number of Real Solutions" ] } ## Identify the coefficients Using the **Quadratic Equations** knowledge point $$ \begin{aligned} &a = 1\ &b = 9\ &c = 10 \end{aligned} $$ ## Calculate the discriminant Using the **Discriminant of Quadratic** knowledge point $$ \begin{aligned} \Delta &= b^2 - 4ac\ &= 9^2 - 4(1)(10)\ &= 81 - 40\ &= 41 \end{aligned} $$ ## Determine the nature of the roots Using the **Number of Real Solutions** knowledge point $$ \begin{aligned} &\Delta = 41 > 0 \implies \text{Two distinct real roots} \end{aligned} $$

Real and equal

Real and distinct

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

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QUESTION IMAGE

Question

Explanation:

Identify the coefficients

Calculate the discriminant

Determine the nature of the roots

Answer: