solve: (3x^2 - x - 2 = 0)

(write your answer as a fraction if applicable)

(x =) or (x =)

Question

solve: (3x^2 - x - 2 = 0)

(write your answer as a fraction if applicable)

(x =)   or (x =)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Factoring", "Solving for Variables" ], "new_concepts": [ "Quadratic Equations" ], "current_concepts": [ "Quadratic Factoring", "Solving for Variables", "Quadratic Equations" ] } ## Factor the quadratic equation $$ \begin{aligned} 3x^2 - x - 2 &= 0 \ 3x^2 - 3x + 2x - 2 &= 0 \ 3x(x - 1) + 2(x - 1) &= 0 \ (3x + 2)(x - 1) &= 0 \end{aligned} $$ ## Solve for the roots $$ \begin{aligned} 3x + 2 = 0 &\implies x = -\frac{2}{3} \ x - 1 = 0 &\implies x = 1 \end{aligned} $$ Solve: $3x^2 - x - 2 = 0$ $x =$ $-\frac{2}{3}$ or $x =$ $1$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Equations" ] }

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Factor the quadratic equation

Solve for the roots

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