StudyGPT Just Leveled Up – Say Hello to Knowee! 🚀
Knowee
Questions
Features
Study Tools

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

Question

🧐 Not the exact question you are looking for?Go ask a question

Solution

1. Break Down the Problem

We need to find the solution set of the quadratic equation x2+5x+6=0x^2 + 5x + 6 = 0. This involves identifying the roots of the equation.

2. Relevant Concepts

To solve the quadratic equation of the form ax2+bx+c=0ax^2 + bx + c = 0, we can use the factoring method or apply the quadratic formula: x=b±b24ac2a x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} In this case, a=1a = 1, b=5b = 5, and c=6c = 6.

3. Analysis and Detail

  1. Calculate the Discriminant: D=b24ac=52416=2524=1 D = b^2 - 4ac = 5^2 - 4 \cdot 1 \cdot 6 = 25 - 24 = 1

  2. Compute the Roots Using the Quadratic Formula: x=5±121=5±12 x = \frac{{-5 \pm \sqrt{1}}}{{2 \cdot 1}} = \frac{{-5 \pm 1}}{2} This gives us two potential solutions: x1=5+12=42=2 x_1 = \frac{{-5 + 1}}{2} = \frac{{-4}}{2} = -2 x2=512=62=3 x_2 = \frac{{-5 - 1}}{2} = \frac{{-6}}{2} = -3

4. Verify and Summarize

The roots of the equation are x=2x = -2 and x=3x = -3. Therefore, the solution set for the equation x2+5x+6=0x^2 + 5x + 6 = 0 is {2,3}\{-2, -3\}.

Final Answer

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

This problem has been solved

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.