Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am solving the following inequality, please look at it and tell me whether am I correct or not. This is an example in Howard Anton's book and I solved it on my own as given below, but the book has solved it differently! I want to confirm that my solution is also valid.

alt text

share|improve this question
Hint: if both x-5 and x+2 have the same sign (positive or negative), their product will be greater than 0. –  Guess who it is. Aug 15 '10 at 12:35
Just so you know: "Hay" is properly spelled "Hey" and "Hey Dear" is generally only used between married couples. On a forum, you should introduce yourself using either simply "Hey" or "Hey everyone". On Stack Exchange, you don't need to "Hey" at all, you can just post your problem and your motivation –  Casebash Aug 15 '10 at 12:39
oo exelent sir, thank you. –  Zia ur Rahman Aug 15 '10 at 12:49
Exelent should be excellent. Next time, when you post a thread just say something regarding the question. You don't need to use hey,hi sort of things while posting the question. –  anonymous Aug 15 '10 at 12:55
I don't see this is a (differential and integral) calculus question. Why was the calculus tag used?. –  Américo Tavares Aug 15 '10 at 17:33

3 Answers 3

up vote 5 down vote accepted

For ab to be positive either

  • a and b are both positive
  • a and b are both negative

Here, a=x-5 and b=x+2

They are both positive if x>5. They are both negative if x<-2. Either of these will solve the problem

share|improve this answer
Remove the "non" part in your answer and it becomes accurate; what he has is a strict inequality (">" instead of "≥") –  Guess who it is. Aug 15 '10 at 12:37
@J. You are right, I misread the problem –  Casebash Aug 15 '10 at 12:42
Thank you Sir i have understood it know. –  Zia ur Rahman Aug 15 '10 at 12:43

If you graph the function $y=x^2-3x-10$, you can see that the solution is $x<-2$ or $x>5$.

alt text

share|improve this answer
image failure!! –  The Chaz 2.0 Sep 15 '11 at 13:23

Casebash's answer is very good.

Here is a second answer. You can apply the following

Theorem: If the roots $x_{1},x_{2}$ of $f(x)=ax^{2}+bx+c$ are real and $x_{1}\neq x_{2}$ (with $x_{1} < x_{2}$), then, the signal of $f(x)$ is:

  • opposite to the signal of $a$ for $x\in \left[ x_{1},x_{2}\right] $,
  • the same of $a$ for $x\in \left] -\infty ,x_{1}\right[ \vee x\in \left] x_{2},-\infty \right[ $.

Since in your case $a=1>0$, $x_{1}=-2<5=x_{2}$, you have $x^{2}-3x-10>0$ for $x\in \left] -\infty ,-2\right[ \vee x\in \left] 5,\infty \right[ $.

Addendum: A possible proof of this theorem is to use the explanation of Casebash, taking into consideration that $ax^{2}+bx+c=a(x-x_1)(x-x_2)$

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.