Highest and least value of 4x^2 in the the inequation

Question

anonymous · Answer

sry wait typing the question

parthkohli · Answer

I've seen all of these questions in my coaching module. o.O

parthkohli · Answer

Since No.Name isn't here, I'll type the question out...

parthkohli · Answer

$$\dfrac{6x^2 - 5x - 3}{x^2 - 2x + 6} \le 4$$

parthkohli · Answer

What did you get for the solution set of $x$?

anonymous · Answer

My cputer hanged , sry 
yes that is the question

parthkohli · Answer

OK, your first step is to solve the inequality...

anonymous · Answer

I am stuck on this step
$$\huge \frac{ 2x^2 +3x-27 }{ x^2-2x+6 } <=0$$

anonymous · Answer

They can't be perfectly factorized , o have I done a very silly mistake

parthkohli · Answer

The denominator is always positive, so you can just remove it from the inequality.

anonymous · Answer

yeah
$$\huge2x^2+3x-27 \le 0$$

parthkohli · Answer

Great, factorize.

anonymous · Answer

one oot is in decimal;s

parthkohli · Answer

Yeah.$$2x^2 + 9x - 6x - 27 = x(2x + 9) - 3(2x + 9)  = (x-3)(2x+9) \le 0$$$$x \in \left(-\frac{9}{2},3\right)$$

parthkohli · Answer

Now is the fun part.

anonymous · Answer

Actually
$$\huge [-4.5 , 3]$$, they are included

parthkohli · Answer

Argh, OS is buggy.

Yeah - I was correcting that.

anonymous · Answer

but weird answer is given

parthkohli · Answer

No...

parthkohli · Answer

Do you know how $|x|^2 = x^2$?

anonymous · Answer

yup

anonymous · Answer

I am getting 36 and 81

parthkohli · Answer

So if a number has the highest modulus, then its square will be the highest. Which means that -4.5 has a bigger modulus than 3, so it has the highest square in the solution set of x, meaning that it has the highest four times the square...

parthkohli · Answer

Similarly the number with the least modulus in the solution set of x is 0, so it is supposed to have the least square, and also the least four-times-the-square.

parthkohli · Answer

You got the 81 right.

anonymous · Answer

oh fu**k

parthkohli · Answer

You mean fu*k.

anonymous · Answer

wtf man , I didn't realize that , I plugged in the exteme values lol

parthkohli · Answer

lol

anonymous · Answer

0 is a cruel number 
thank you  , !

parthkohli · Answer

Ancient Indians are coming to kill you. :P

anonymous · Answer

rofl

ikram002p · Answer

0 :D is my favorite nothing :P

anonymous · Answer

because you get it on your exam am I right?

ikram002p · Answer

xD lol

anonymous · Answer

Nothing is your favourite yet something's you favourite because Hamiltonian of thoughts can never be 0 @ikram002p

anonymous · Answer

just jokin, hehe

ikram002p · Answer

ik udit :P but still a nice joke