select the correct answer.

what are the solutions of the quadratic equation below?

\4x^2 - 30x + 45 = 0\

$\bigcirc$ $\frac{-15 \pm 6\sqrt{5}}{4}$

$\bigcirc$ $\frac{15 \pm 6\sqrt{5}}{4}$

$\bigcirc$ $\frac{15 \pm 3\sqrt{5}}{4}$

$\bigcirc$ $\frac{30 \pm 3\sqrt{5}}{4}$

Question

select the correct answer.

what are the solutions of the quadratic equation below?

\4x^2 - 30x + 45 = 0\

$\bigcirc$ $\frac{-15 \pm 6\sqrt{5}}{4}$

$\bigcirc$ $\frac{15 \pm 6\sqrt{5}}{4}$

$\bigcirc$ $\frac{15 \pm 3\sqrt{5}}{4}$

$\bigcirc$ $\frac{30 \pm 3\sqrt{5}}{4}$

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" ], "new_concepts": [], "current_concepts": [ "Quadratic Formula Application", "Quadratic Functions" ] } ## Identify coefficients of the quadratic equation $$ \begin{aligned} &a = 4 \ &b = -30 \ &c = 45 \end{aligned} $$ ## Apply the quadratic formula $$ \begin{aligned} x &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ x &= \frac{-(-30) \pm \sqrt{(-30)^2 - 4(4)(45)}}{2(4)} \ x &= \frac{30 \pm \sqrt{900 - 720}}{8} \ x &= \frac{30 \pm \sqrt{180}}{8} \end{aligned} $$ ## Simplify the radical and fraction $$ \begin{aligned} \sqrt{180} &= \sqrt{36 \times 5} = 6\sqrt{5} \ x &= \frac{30 \pm 6\sqrt{5}}{8} \ x &= \frac{2(15 \pm 3\sqrt{5})}{8} \ x &= \frac{15 \pm 3\sqrt{5}}{4} \end{aligned} $$

(A) $\frac{-15 \pm 6\sqrt{5}}{4}$

(B) $\frac{15 \pm 6\sqrt{5}}{4}$

(C) $\frac{15 \pm 3\sqrt{5}}{4}$

(D) $\frac{30 \pm 3\sqrt{5}}{4}$

{ "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 fraction

Answer: