select the correct answer.

what are the solutions of this quadratic equation?

(x^2 + 8x + 3 = 0)

(x = 4 \pm \sqrt{13})

(x = 8 \pm 2\sqrt{13})

(x = -8 \pm 2\sqrt{13})

(x = -4 \pm \sqrt{13})

Question

select the correct answer.

what are the solutions of this quadratic equation?

(x^2 + 8x + 3 = 0)

(x = 4 \pm \sqrt{13})

(x = 8 \pm 2\sqrt{13})

(x = -8 \pm 2\sqrt{13})

(x = -4 \pm \sqrt{13})

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", "Completing the Square" ], "new_concepts": [], "current_concepts": [ "Quadratic Equations", "Quadratic Formula Application", "Completing the Square" ] } ## Identify coefficients of the quadratic equation $$ \begin{aligned} &a = 1 \ &b = 8 \ &c = 3 \end{aligned} $$ ## Apply the quadratic formula $$ \begin{aligned} x &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ x &= \frac{-8 \pm \sqrt{8^2 - 4(1)(3)}}{2(1)} \ x &= \frac{-8 \pm \sqrt{64 - 12}}{2} \ x &= \frac{-8 \pm \sqrt{52}}{2} \end{aligned} $$ ## Simplify the radical and expression $$ \begin{aligned} \sqrt{52} &= \sqrt{4 \times 13} = 2\sqrt{13} \ x &= \frac{-8 \pm 2\sqrt{13}}{2} \ x &= -4 \pm \sqrt{13} \end{aligned} $$

(A) $x = 4 \pm \sqrt{13}$

(B) $x = 8 \pm 2\sqrt{13}$

(C) $x = -8 \pm 2\sqrt{13}$

(D) $x = -4 \pm \sqrt{13}$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify coefficients of the quadratic equation

Apply the quadratic formula

Simplify the radical and expression

Answer: