select the correct answer.

what are the roots of this quadratic equation?

\3x^2 + 10 = 4x\

$x = \frac{2 \pm i\sqrt{26}}{2}$

$x = \frac{-2 \pm i\sqrt{26}}{3}$

$x = -4 \pm 6i\sqrt{26}$

$x = \frac{2 \pm i\sqrt{26}}{3}$

Question

select the correct answer.

what are the roots of this quadratic equation?

\3x^2 + 10 = 4x\

$x = \frac{2 \pm i\sqrt{26}}{2}$

$x = \frac{-2 \pm i\sqrt{26}}{3}$

$x = -4 \pm 6i\sqrt{26}$

$x = \frac{2 \pm i\sqrt{26}}{3}$

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", "Complex Number Arithmetic" ], "new_concepts": [], "current_concepts": [ "Quadratic Formula Application", "Complex Number Arithmetic", "Quadratic Functions" ] } ## Rearrange the quadratic equation into standard form $$ \begin{aligned} 3x^2 + 10 &= 4x \ 3x^2 - 4x + 10 &= 0 \end{aligned} $$ ## Apply the quadratic formula $$ \begin{aligned} a &= 3,\quad b = -4,\quad c = 10 \ x &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ x &= \frac{-(-4) \pm \sqrt{(-4)^2 - 4(3)(10)}}{2(3)} \ x &= \frac{4 \pm \sqrt{16 - 120}}{6} \ x &= \frac{4 \pm \sqrt{-104}}{6} \end{aligned} $$ ## Simplify the radical and complex expression $$ \begin{aligned} \sqrt{-104} &= i\sqrt{104} = i\sqrt{4 \times 26} = 2i\sqrt{26} \ x &= \frac{4 \pm 2i\sqrt{26}}{6} \ x &= \frac{2(2 \pm i\sqrt{26})}{6} \ x &= \frac{2 \pm i\sqrt{26}}{3} \end{aligned} $$

(A) $x = \frac{2 \pm i\sqrt{26}}{2}$

(B) $x = \frac{-2 \pm i\sqrt{26}}{3}$

(C) $x = -4 \pm 6i\sqrt{26}$

(D) $x = \frac{2 \pm i\sqrt{26}}{3}$

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

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QUESTION IMAGE

Question

Explanation:

Rearrange the quadratic equation into standard form

Apply the quadratic formula

Simplify the radical and complex expression

Answer: