how many real zeros does the following quadratic function have?

\f(x) = -7x^2 + 9x - 5\

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

- one real zero
- two real zeros
- no real zeros

Question

how many real zeros does the following quadratic function have?

\f(x) = -7x^2 + 9x - 5\

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

- one real zero
- two real zeros
- no 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 coefficients of the quadratic function Using the **Standard Form of a Quadratic** knowledge point $$ \begin{aligned} &f(x) = ax^2 + bx + c\ &a = -7,\quad b = 9,\quad c = -5 \end{aligned} $$ ## Calculate the discriminant Using the *Discriminant Analysis* knowledge point $$ \begin{aligned} D &= b^2 - 4ac\ D &= 9^2 - 4(-7)(-5)\ D &= 81 - 140\ D &= -59 \end{aligned} $$ ## Determine the number of real zeros Using the *Number of Quadratic Solutions* knowledge point $$ \begin{aligned} &D = -59 < 0\ &\text{Since } D < 0, \text{ there are no real zeros.} \end{aligned} $$

one real zero

two real zeros

no real zeros

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

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Question

Explanation:

Identify coefficients of the quadratic function

Calculate the discriminant

Determine the number of real zeros

Answer: