which equation shows the quadratic formula used correctly to solve (5x^2 + 3x - 4 = 0) for (x)?

(x = \frac{-3 \pm \sqrt{(3)^2 - 4(5)(-4)}}{2(5)})

(x = \frac{3 \pm \sqrt{(3)^2 + 4(5)(-4)}}{2(5)})

(x = \frac{3 \pm \sqrt{(3)^2 - 4(5)(-4)}}{2(5)})

(x = \frac{-3 \pm \sqrt{(3)^2 + 4(5)(-4)}}{2(5)})

Question

which equation shows the quadratic formula used correctly to solve (5x^2 + 3x - 4 = 0) for (x)?

(x = \frac{-3 \pm \sqrt{(3)^2 - 4(5)(-4)}}{2(5)})

(x = \frac{3 \pm \sqrt{(3)^2 + 4(5)(-4)}}{2(5)})

(x = \frac{3 \pm \sqrt{(3)^2 - 4(5)(-4)}}{2(5)})

(x = \frac{-3 \pm \sqrt{(3)^2 + 4(5)(-4)}}{2(5)})

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Formula Application" ], "new_concepts": [], "current_concepts": [ "Quadratic Formula Application" ] } ## Identify coefficients of the quadratic equation $$ \begin{aligned} &ax^2 + bx + c = 0 \ &5x^2 + 3x - 4 = 0 \ &a = 5,\quad b = 3,\quad c = -4 \end{aligned} $$ ## Substitute coefficients into the quadratic formula $$ \begin{aligned} &x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ &x = \frac{-(3) \pm \sqrt{(3)^2 - 4(5)(-4)}}{2(5)} \end{aligned} $$

(A) $x = \frac{-3 \pm \sqrt{(3)^2 - 4(5)(-4)}}{2(5)}$

(B) $x = \frac{3 \pm \sqrt{(3)^2 + 4(5)(-4)}}{2(5)}$

(C) $x = \frac{3 \pm \sqrt{(3)^2 - 4(5)(-4)}}{2(5)}$

(D) $x = \frac{-3 \pm \sqrt{(3)^2 + 4(5)(-4)}}{2(5)}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Formula Application" ] }

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QUESTION IMAGE

Question

Explanation:

Identify coefficients of the quadratic equation

Substitute coefficients into the quadratic formula

Answer: