Question

question 40 points 3 solve the quadratic equation $5x^2 + x + 1 = 0$ using the quadratic formula. $\bigcirc$ $x = \frac{-1 \pm i\sqrt{19}}{10}$ $\bigcirc$ $x = \frac{-1 \pm i\sqrt{20}}{10}$ $\bigcirc$ $x = \frac{-1 \pm i\sqrt{19}}{5}$ $\bigcirc$ $x = \frac{-5 \pm i\sqrt{19}}{10}$

Explanation:

Step1: Identify quadratic coefficients

For $5x^2 + x + 1 = 0$, $a=5$, $b=1$, $c=1$

Step2: Calculate discriminant

$\Delta = b^2 - 4ac = 1^2 - 4(5)(1) = 1 - 20 = -19$

Step3: Apply quadratic formula

Quadratic formula: $x = \frac{-b \pm \sqrt{\Delta}}{2a}$
Substitute values: $x = \frac{-1 \pm \sqrt{-19}}{2(5)} = \frac{-1 \pm i\sqrt{19}}{10}$

Answer:

$\boldsymbol{x = \frac{-1 \pm i\sqrt{19}}{10}}$ (matches the first option)