which are the solutions of (3x^2 - 2x - 5 = 0) by factoring?

a. (-5, \frac{1}{3})

b. (-1, \frac{5}{3})

c. (-1, -\frac{5}{3})

d. (5, \frac{1}{3})

Question

which are the solutions of (3x^2 - 2x - 5 = 0) by factoring?

a. (-5, \frac{1}{3})

b. (-1, \frac{5}{3})

c. (-1, -\frac{5}{3})

d. (5, \frac{1}{3})

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Factoring Quadratics", "Solving Quadratic Equations" ], "new_concepts": [], "current_concepts": [ "Factoring Quadratics", "Solving Quadratic Equations" ] } ## Factor the quadratic expression $$ \begin{aligned} &3x^2 - 2x - 5 = 0 \ &3x^2 - 5x + 3x - 5 = 0 \ &x(3x - 5) + 1(3x - 5) = 0 \ &(3x - 5)(x + 1) = 0 \end{aligned} $$ ## Solve for x $$ \begin{aligned} &3x - 5 = 0 \implies x = \frac{5}{3} \ &x + 1 = 0 \implies x = -1 \end{aligned} $$

A. $-5, \frac{1}{3}$

B. $-1, \frac{5}{3}$

C. $-1, -\frac{5}{3}$

D. $5, \frac{1}{3}$

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

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