Question

I need a function of x that is equal to zero at x = -1 and x = 1, also it needs to be negative on (-infinity, -1)U(-1,1) and positive on (1, infinity)

Answer 1

Since you want it to be negative on the interval (-infinity, -1)U(-1,1) this means that it must just touch the x-axis at that point, and then go back down at x=-1. This means that the zero at -1 must have multiplicity two. Hence, your function could be \[(x+1)^2(x-1)=x^3+x^2-x-1\]

Answer 2

ty

Answer 3

You're welcome.