f(x) = (x-1)^3(x+2)^4(x-3)^5(x+6)/x^2(x-7)^3 then find the interval in which f(x) is (a) greater than zero (b)greater or equal to zero . please tell me when values of x are pointed on no line , then how to detect that which segment is posi. or nega .

Hi,

We are goin to follow the wavey curve method to answer this question. I hope u are aware of this method.

The reeots are as follows 1, -2, 3, -6, 0, 7
Also 1 has odd no of roots (i.e. sign change) and also 3, -6, 7 have odd no of roots at that values
Similarly -2, and 0 has even no of roots ie.e no sign change.

So grater than zero : (-inf to -6) U (1,3) U (7 to inf)
Grater than /equal to zero : (-inf to -6] U [1,3] U (7 to inf)

mind the bracketts