plz explain wavy curve method nd Modulus in mathematics 2 me as soon as possible

Dear Deepanshu Mohan,

If Suppose you have a polynomial function, (ax+b)(cx+d)....... ,
and you  would like to know where the function is +ve or -ve( on the real line of course) just arrange the roots in ascending order as on the no line.
Start from the rightmost root.All values of the function for x greater than this root are +ve.Then in the interval between the largest and second largest the value is -ve and its goes on alternating between the roots. 

For example , take the case of x(3x+1)(3x-1),
The roots are -1/3,0,1/3.
x > 1/3 => expression +ve
0< x < 1/3 => -ve
-1/3< x < 0 =>+ve
x<-1/3 => -ve

Its called wavy curve because you can draw something like a worm curving its body on the no line.

Hope this helped you immensely..

All the Very Best & Good Luck to you ...

Regards,

AskIITians Expert,

Godfrey Classic Prince

IIT-M

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