the graph of (f(x) = 2x^2 + 23x - 39) passes through the point ((0, -39)) and one of its zeros is ((-13, 0)). what is the other zero of the function?

a. 0
b. (\frac{2}{3})
c. (\frac{3}{2})
d. 3

Question

the graph of (f(x) = 2x^2 + 23x - 39) passes through the point ((0, -39)) and one of its zeros is ((-13, 0)). what is the other zero of the function?

a. 0
b. (\frac{2}{3})
c. (\frac{3}{2})
d. 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" ], "new_concepts": [], "current_concepts": [ "Factoring Quadratics", "Finding Quadratic Equations" ] } ## Set the quadratic function to zero $$ 2x^2 + 23x - 39 = 0 $$ ## Factor the quadratic equation $$ (2x - 3)(x + 13) = 0 $$ ## Solve for the zeros $$ \begin{aligned} 2x - 3 = 0 &\implies x = \frac{3}{2} \ x + 13 = 0 &\implies x = -13 \end{aligned} $$

A. 0

B. $\frac{2}{3}$

C. $\frac{3}{2}$

D. 3

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Quadratics" ] }

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QUESTION IMAGE

Question

Explanation:

Set the quadratic function to zero

Factor the quadratic equation

Solve for the zeros

Answer: