6 Determine the Most Efficient Method to Use When Solving a Quadratic Equation
-$$6 x ^ { 2 } + 12 x + 3 = 0$$
A) $\left\{ \frac { - 2 - \sqrt { 2 } } { 2 } , \frac { - 2 + \sqrt { 2 } } { 2 } \right\}$
B) $\left\{ \frac { - 2 - \sqrt { 2 } } { 12 } , \frac { - 2 + \sqrt { 2 } } { 12 } \right\}$
C) $\left\{ \frac { - 12 - \sqrt { 2 } } { 2 } , \frac { - 12 + \sqrt { 2 } } { 2 } \right\}$
D) $\left\{ \frac { - 2 - \sqrt { 6 } } { 2 } , \frac { - 2 + \sqrt { 6 } } { 2 } \right\}$

Question

Quizplus · Accepted Answer

The quadratic equation can be solved using the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. Plugging in the values of a, b, and c from the given equation, we get: $x = \frac{-12 \pm \sqrt{12^2 - 4(6)(3)}}{2(6)}$. Simplifying this expression, we get: $x = \frac{-12 \pm \sqrt{144 - 72}}{12}$. Further simplifying, we get: $x = \frac{-12 \pm \sqrt{72}}{12}$. Finally, simplifying one last time, we get: $x = \frac{-12 \pm 6\sqrt{2}}{12}$. Dividing both the numerator and denominator by 6, we get: $x = \frac{-2 \pm \sqrt{2}}{2}$. Therefore, the correct answer is A.

6 Determine the Most Efficient Method to Use When Solving 6x2+12x+3=06 x ^ { 2 } + 12 x + 3 = 06x2+12x+3=0

6 Determine the Most Efficient Method to Use When Solving $6 x ^ { 2 } + 12 x + 3 = 0$