We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
142
5
avatar

This is due in a few hours, so I really need quick help. I was undergoing surgery so I couldn't go to a class called art of problem solving online. There are online classes and I was not able to participate in the class. I know nothing about the unit for this week and need help with solving just one problem. I generally don't like doing this, but I also want to understand how to do the problem.

 

The question:

(x^2 + x + 3)/(2x^2 + x - 6) ≥ 0.

 

Please also explain how to solve this so that I can understand this unit. Thanks, I will be so happy if somebody answers this.

 Feb 24, 2019
 #1
avatar+6045 
0

\(\text{surgery eh...}\\ x^2 + x + 3 = \left(x+\dfrac 1 2\right)^2 +\dfrac{11}{4} >0\\ 2x^2 + x - 6 = (2x-3 )(x+2)\\ 2x^2 + x - 6 \begin{cases}+ &x<2\\0&x=2\\- &2 < x < \dfrac 3 2\\ 0 &x=\dfrac 3 2\\+&\dfrac 3 2 < x\end{cases}\)

 

\(+ \div + \Rightarrow +\\ +\div - \Rightarrow -\\ \dfrac{x^2+x+3}{2x^2+x-6}\geq 0 \Rightarrow (-\infty,2]\cup \left[\dfrac 3 2,\infty\right)\)

.
 Feb 24, 2019
 #2
avatar
0

Yeah, it was a snorkeling accident with coral. Thanks so much though!

Guest Feb 24, 2019
 #3
avatar
0

Wait, I have one quick question. I do not get your solution. I want to understand the problem so I am wondering if you could tell me a tiny bit more about the step where you have the equation 2x^2 + x - 6 and the +, -, and 0's.

 

Why is there 2 differnet 0's and +'s?

 

You were very helpful, thanks for answering my question.

Guest Feb 24, 2019
 #4
avatar+6045 
0

that just denotes where the polynomial is positive, zero, and negative

 

the numerator is always positive.

 

pos/pos = pos

 

pos/neg = neg

Rom  Feb 24, 2019

36 Online Users