select the correct answer.

which statement is true about this quadratic equation?
\y = -2x^2 + 9x - 12\

there is one complex solution.
there are two real solutions.
there is one real solution.
there are two complex solutions.

Question

select the correct answer.

which statement is true about this quadratic equation?
\y = -2x^2 + 9x - 12\

there is one complex solution.
there are two real solutions.
there is one real solution.
there are two complex solutions.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Functions", "Quadratic Formula Application" ], "new_concepts": [ "Discriminant of a Quadratic" ], "current_concepts": [ "Quadratic Functions", "Quadratic Formula Application", "Discriminant of a Quadratic" ] } ## Identify the coefficients of the quadratic equation $$ \begin{aligned} &y = -2x^2 + 9x - 12 \ &a = -2, \quad b = 9, \quad c = -12 \end{aligned} $$ ## Calculate the discriminant $$ \begin{aligned} D &= b^2 - 4ac \ D &= 9^2 - 4(-2)(-12) \ D &= 81 - 96 \ D &= -15 \end{aligned} $$ ## Determine the nature of the solutions $$ \begin{aligned} &D < 0 \implies \text{Two complex solutions} \end{aligned} $$

There is one complex solution.

There are two real solutions.

There is one real solution.

There are two complex solutions.

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

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QUESTION IMAGE

Question

Explanation:

Identify the coefficients of the quadratic equation

Calculate the discriminant

Determine the nature of the solutions

Answer: