which equation has the solutions $x = \frac{5 \pm 2\sqrt{7}}{3}$?

$3x^2 - 5x + 7 = 0$
$3x^2 - 5x - 1 = 0$
$3x^2 - 10x + 6 = 0$
$3x^2 - 10x - 1 = 0$

Question

which equation has the solutions $x = \frac{5 \pm 2\sqrt{7}}{3}$?

$3x^2 - 5x + 7 = 0$
$3x^2 - 5x - 1 = 0$
$3x^2 - 10x + 6 = 0$
$3x^2 - 10x - 1 = 0$

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", "Solving Quadratic Equations" ], "new_concepts": [], "current_concepts": [ "Quadratic Formula Application", "Solving Quadratic Equations" ] } ## Isolate the radical term $$ \begin{aligned} x &= \frac{5 \pm 2\sqrt{7}}{3} \ 3x &= 5 \pm 2\sqrt{7} \ 3x - 5 &= \pm 2\sqrt{7} \end{aligned} $$ ## Square both sides of the equation $$ \begin{aligned} (3x - 5)^2 &= (\pm 2\sqrt{7})^2 \ 9x^2 - 30x + 25 &= 4 \cdot 7 \ 9x^2 - 30x + 25 &= 28 \end{aligned} $$ ## Rearrange into standard quadratic form $$ \begin{aligned} 9x^2 - 30x - 3 &= 0 \ 3(3x^2 - 10x - 1) &= 0 \ 3x^2 - 10x - 1 &= 0 \end{aligned} $$

(A) $3x^2 - 5x + 7 = 0$

(B) $3x^2 - 5x - 1 = 0$

(C) $3x^2 - 10x + 6 = 0$

(D) $3x^2 - 10x - 1 = 0$

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

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QUESTION IMAGE

Question

Explanation:

Isolate the radical term

Square both sides of the equation

Rearrange into standard quadratic form

Answer: