Solve for x-- the inequality of quadratic

Solve

------

.'.

and

.'.

then converting the original inequality to

As Discriminant <0 it has no real roots

so how to do further...

My assumptions:-

should not be zero

should also not be zero

Are my assumptions right?

Any help will be highly appreciated.

Re: Solve for x-- the inequality of quadratic

hi sumedh

your "conversion" isn't correct.you cannot multiply an inequality by something you don't know the sign of.

can you do it from here?

Re: Solve for x-- the inequality of quadratic

i am really very thankful to you :)

it will be your greatness if you tell few next steps .

Re: Solve for x-- the inequality of quadratic

If you know:

That means:

Now solve .

What do you notice?

After this you only have to make the sign-table to determine where

Re: Solve for x-- the inequality of quadratic

hi Siron

actually he should make a sign table for:

because (x-3)(x+2)(x+3) might be negative and thus change the sign of the inequality.so we mustn't multiply by (x-3)(x+2)(x+3).

Re: Solve for x-- the inequality of quadratic

Yes, I ment that but maybe I had better said:

Re: Solve for x-- the inequality of quadratic

x^2+4x+9=0 has imaginary roots.

so it will be always positive

and we will have to consider the denominator now, right??

Re: Solve for x-- the inequality of quadratic

Indeed , an easy way to determine this statement is by using completing the square:

Which is always true!

Go on with the denominator.

Re: Solve for x-- the inequality of quadratic

Re: Solve for x-- the inequality of quadratic

Okay, you're welcome and good work! :)