The solution set of x^2 + 5x + 6 = 0Question 1Answera.∅b.{-1 ,6 }c.{-2 ,-3 }d.{2 ,3 }

1. Break Down the Problem

We need to find the solution set of the quadratic equation $x^2 + 5x + 6 = 0$. This involves identifying the roots of the equation.

2. Relevant Concepts

To solve the quadratic equation of the form $ax^2 + bx + c = 0$, we can use the factoring method or apply the quadratic formula: $x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$ In this case, $a = 1$, $b = 5$, and $c = 6$.

3. Analysis and Detail

1. Calculate the Discriminant: $D = b^2 - 4ac = 5^2 - 4 \cdot 1 \cdot 6 = 25 - 24 = 1$

2. Compute the Roots Using the Quadratic Formula: $x = \frac{{-5 \pm \sqrt{1}}}{{2 \cdot 1}} = \frac{{-5 \pm 1}}{2}$ This gives us two potential solutions: $x_1 = \frac{{-5 + 1}}{2} = \frac{{-4}}{2} = -2$ $x_2 = \frac{{-5 - 1}}{2} = \frac{{-6}}{2} = -3$

4. Verify and Summarize

The roots of the equation are $x = -2$ and $x = -3$. Therefore, the solution set for the equation $x^2 + 5x + 6 = 0$ is $\{-2, -3\}$.

Final Answer

The final solution set is $\{-2, -3\}$, corresponding to option c.