arpanpatnaik wrote:
Totally agree with Zarrolou!
Would like to add an observation which would help you over such inequalities. In general, when you look at functions, such as
F(x) > 0 where F(x) may be a mod function or quadratic equation, you would always arrive at an open-ended solution set i.e.
{-ve infinity, p1} and {+ve infinity, p2}, where p1 and p2 are roots of the equation F(x) = 0.
So whenever you see such an quadratic equation, and you calculate the roots, you can plug them in the above range and determine a solution set!
Similarly, for functions of the form, F(x) < 0 the solution set is always of the form {p1,p2} and is a closed-set! You can go ahead and test the theory over as many equations you like! The above idea is extremely useful in determining quick answers to such inequality questions!
Hope it helps!
Regards,
Arpan
I am afraid but I have to disagree with you.
"F(x) > 0 where F(x) may be a mod function or quadratic equation, you would always arrive at an open-ended solution set"
This is not true: Consider F(x)=-x^2+x for example
if you study F(x)>0 you will arrive at a closed solution
In this particular case is F(x)=-x^2+x>0 or 0<x<1 => closed interval
Also "F(x) < 0 the solution set is always of the form {p1,p2} and is a closed-set" is wrong.
Do you agree?