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}\\) \\(x = \frac{\square}{\square}, \\, x = \frac{\square}{\square}\\)

Explanation:

Step1: Identify quadratic coefficients

For $5x^2 - 8x + 5 = 0$, $a=5$, $b=-8$, $c=5$

Step2: Apply quadratic formula

Quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Substitute values:
$x = \frac{-(-8) \pm \sqrt{(-8)^2 - 4(5)(5)}}{2(5)}$

Step3: Calculate discriminant

$\sqrt{64 - 100} = \sqrt{-36} = 6i$

Step4: Simplify the expression

$x = \frac{8 \pm 6i}{10} = \frac{4 \pm 3i}{5}$

Answer:

$x = \frac{4 - 3i}{5}, x = \frac{4 + 3i}{5}$