2. for what values of x will the function $f(x) = 3x^2 + 13x - 10$ equal zero?

$x = -\frac{2}{3}$ or $5$

$x = 5$ or $-2$

$x = -5$ or $2$

$x = \frac{2}{3}$ or $-5$

Question

2. for what values of x will the function $f(x) = 3x^2 + 13x - 10$ equal zero?

$x = -\frac{2}{3}$ or $5$

$x = 5$ or $-2$

$x = -5$ or $2$

$x = \frac{2}{3}$ or $-5$

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": [ "Solving Quadratic Equations", "Factoring Trinomials", "AC Method", "Zero Product Property" ], "new_concepts": [], "current_concepts": [ "Solving Quadratic Equations", "Factoring Trinomials", "AC Method", "Zero Product Property" ] } ## Set the function equal to zero Using the **Solving Quadratic Equations** knowledge point $$ 3x^2 + 13x - 10 = 0 $$ ## Factor the quadratic expression Using the **Factoring Trinomials** and **AC Method** knowledge points $$ \begin{aligned} &a \cdot c = 3 \cdot (-10) = -30\ &15 \cdot (-2) = -30 \quad \text{and} \quad 15 + (-2) = 13\ &3x^2 + 15x - 2x - 10 = 0\ &3x(x + 5) - 2(x + 5) = 0\ &(3x - 2)(x + 5) = 0 \end{aligned} $$ ## Solve for x Using the **Zero Product Property** knowledge point $$ \begin{aligned} &3x - 2 = 0 \implies x = \frac{2}{3}\ &x + 5 = 0 \implies x = -5 \end{aligned} $$

(A) $x = -\frac{2}{3}$ or $5$

(B) $x = 5$ or $-2$

(C) $x = -5$ or $2$

(D) $x = \frac{2}{3}$ or $-5$

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

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QUESTION IMAGE

Question

Explanation:

Set the function equal to zero

Factor the quadratic expression

Solve for x

Answer: