how many solutions does this quadratic have?
\y = 9x^2 - 49\

one solution

two solutions

Question

how many solutions does this quadratic have?
\y = 9x^2 - 49\

one solution

two solutions

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": [ "Solving Quadratic Equations", "Square Root Property", "Difference of Squares" ], "new_concepts": [ "Number of Quadratic Solutions" ], "current_concepts": [ "Solving Quadratic Equations", "Square Root Property", "Difference of Squares", "Number of Quadratic Solutions" ] } ## Set the quadratic function to zero Using the **Solving Quadratic Equations** knowledge point $$ 9x^2 - 49 = 0 $$ ## Solve using the square root property Using the **Square Root Property** knowledge point $$ \begin{aligned} 9x^2 &= 49 \ x^2 &= \frac{49}{9} \ x &= \pm\sqrt{\frac{49}{9}} \ x &= \pm\frac{7}{3} \end{aligned} $$ ## Determine the number of solutions Using the **Solving Quadratic Equations** knowledge point $$ x_1 = \frac{7}{3}, \quad x_2 = -\frac{7}{3} $$ The equation has exactly two distinct real solutions.

one solution

two solutions

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations" ] }

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Question

Explanation:

Set the quadratic function to zero

Solve using the square root property

Determine the number of solutions

Answer: