Question

select the correct answer.
what are the solutions of this quadratic equation?
x² + 8x + 3 = 0
a. x = 4 ± √13
b. x = 8 ± 2√13
c. x = -8 ± 2√13
d. x = -4 ± √13

Explanation:

Step1: Identify coefficients

For $x^2 + 8x + 3 = 0$, $a=1$, $b=8$, $c=3$.

Step2: Apply quadratic formula

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-8 \pm \sqrt{64 - 12}}{2}$

Step3: Simplify discriminant

$\sqrt{64 - 12} = \sqrt{52} = 2\sqrt{13}$

Step4: Compute final solution

$x = \frac{-8 \pm 2\sqrt{13}}{2} = -4 \pm \sqrt{13}$

Answer:

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