Nguyen Burgess
07/31/2024 · Senior High School
Solve the polynomial inequality and graph the solution set on a real number line. Express the so \( x^{2}+6 x>0 \) Solve the inequality. What is the solution set? Select the correct choice below and, if necessary, A. The solution set is (Simplify your answer. Type your answer in interval notation. Type an exact answer, using the expression.) B. The solution set is the empty set.
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Solve the equation \( x^{2}+6x>0 \).
Solve the inequality by following steps:
- step0: Solve the inequality by testing the values in the interval:
\(x^{2}+6x>0\)
- step1: Rewrite the expression:
\(x^{2}+6x=0\)
- step2: Factor the expression:
\(x\left(x+6\right)=0\)
- step3: Separate into possible cases:
\(\begin{align}&x=0\\&x+6=0\end{align}\)
- step4: Solve the equation:
\(\begin{align}&x=0\\&x=-6\end{align}\)
- step5: Determine the test intervals:
\(\begin{align}&x<-6\\&-60\end{align}\)
- step6: Choose a value:
\(\begin{align}&x_{1}=-7\\&x_{2}=-3\\&x_{3}=1\end{align}\)
- step7: Test the chosen value:
\(\begin{align}&x<-6\textrm{ }\textrm{is the solution}\\&-60\textrm{ }\textrm{is the solution}\end{align}\)
- step8: The final solution is \(x \in \left(-\infty,-6\right)\cup \left(0,+\infty\right):\)
\(x \in \left(-\infty,-6\right)\cup \left(0,+\infty\right)\)
The solution to the polynomial inequality \(x^{2}+6x>0\) is \(x \in (-\infty,-6) \cup (0,+\infty)\).
Therefore, the correct choice is:
A. The solution set is \((- \infty, -6) \cup (0, +\infty)\).
Quick Answer
The solution set is \((- \infty, -6) \cup (0, +\infty)\).
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit