type the correct answer in the box.

solve the following quadratic equation using the quadratic formula.
\5x^2 - 8x + 5 = 0\

write the solutions in the following form, where $r$, $s$, and $t$ are integers, and the fractions are in simplest form.
\x = \frac{r - si}{t}, x = \frac{r + si}{t}\

Question

type the correct answer in the box.

solve the following quadratic equation using the quadratic formula.
\5x^2 - 8x + 5 = 0\

write the solutions in the following form, where $r$, $s$, and $t$ are integers, and the fractions are in simplest form.
\x = \frac{r - si}{t}, x = \frac{r + si}{t}\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Formula", "Complex Roots" ], "new_concepts": [], "current_concepts": [ "Quadratic Formula", "Complex Roots", "Solving Quadratic Equations" ] } ## Identify coefficients from the quadratic equation $$ \begin{aligned} &5x^2 - 8x + 5 = 0 \ &a = 5, \quad b = -8, \quad c = 5 \end{aligned} $$ ## Apply the quadratic formula $$ \begin{aligned} x &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ x &= \frac{-(-8) \pm \sqrt{(-8)^2 - 4(5)(5)}}{2(5)} \ x &= \frac{8 \pm \sqrt{64 - 100}}{10} \ x &= \frac{8 \pm \sqrt{-36}}{10} \end{aligned} $$ ## Simplify the complex roots $$ \begin{aligned} x &= \frac{8 \pm 6i}{10} \ x &= \frac{4 \pm 3i}{5} \ x &= \frac{4 - 3i}{5}, \quad x = \frac{4 + 3i}{5} \end{aligned} $$ Solve the following quadratic equation using the quadratic formula. $$5x^2 - 8x + 5 = 0$$ Write the solutions in the following form, where $r$, $s$, and $t$ are integers, and the fractions are in simplest form. $$x = \frac{r-si}{t}, x = \frac{r+si}{t}$$ $x =$ $\frac{4-3i}{5}$, $x =$ $\frac{4+3i}{5}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Formula" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify coefficients from the quadratic equation

Apply the quadratic formula

Simplify the complex roots

Answer: