Question

question 39 points 3 what are the solutions of the quadratic equation $x^2 + 3x + 12 = 0$? $\frac{-3 \pm i\sqrt{39}}{3}$ $\frac{-3 \pm 3i\sqrt{39}}{2}$ $\frac{3 \pm i\sqrt{39}}{2}$ $\frac{-3 \pm i\sqrt{39}}{2}$

Explanation:

Step1: Identify quadratic coefficients

For $x^2 + 3x + 12 = 0$, $a=1$, $b=3$, $c=12$

Step2: Calculate discriminant

$\Delta = b^2 - 4ac = 3^2 - 4(1)(12) = 9 - 48 = -39$

Step3: Apply quadratic formula

Quadratic formula: $x = \frac{-b \pm \sqrt{\Delta}}{2a}$
Substitute values: $x = \frac{-3 \pm \sqrt{-39}}{2(1)} = \frac{-3 \pm i\sqrt{39}}{2}$

Answer:

$\frac{-3 \pm i\sqrt{39}}{2}$ (the fourth option)