Determine the Most Efficient Method to Use When Solving a Quadratic Equation
Solve the equation by the method of your choice.
-$$6 x ^ { 2 } + 12 x + 1 = 0$$
A) $\left\{ \frac { - 6 - \sqrt { 30 } } { 6 } , \frac { - 6 + \sqrt { 30 } } { 6 } \right\}$
B) $\left\{ \frac { - 6 - \sqrt { 30 } } { 12 } , \frac { - 6 + \sqrt { 30 } } { 12 } \right\}$
C) $\left\{ \frac { - 12 - \sqrt { 30 } } { 6 } , \frac { - 12 + \sqrt { 30 } } { 6 } \right\}$
D) $\left\{ \frac { - 6 - \sqrt { 42 } } { 6 } , \frac { - 6 + \sqrt { 42 } } { 6 } \right\}$

Question

Quizplus · Accepted Answer

The most efficient method to use when solving a quadratic equation is usually factoring or using the quadratic formula. In this case, factoring doesn't seem to be a viable option, so we will use the quadratic formula:

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

In our equation, $a$ is 6, $b$ is 12, and $c$ is 1. Substituting these values into the formula, we get:

$$x=\frac{-12\pm\sqrt{12^2-4(6)(1)}}{2(6)}$$

Simplifying:

$$x=\frac{-12\pm\sqrt{144-24}}{12}$$

$$x=\frac{-12\pm\sqrt{120}}{12}$$

$$x=\frac{-6\pm\sqrt{30}}{6}$$

Therefore, the solutions are $\frac{-6-\sqrt{30}}{6}$ and $\frac{-6+\sqrt{30}}{6}$ or in simplified form, $\left\{\frac{-6-\sqrt{30}}{6},\frac{-6+\sqrt{30}}{6}\right\}$. The answer is choice A.