Get equation for a curve which intersects x at seemingly randomly distributed points? Is there any type of function that when graphed would show a curve which intersects the x axis multiple times, with each point being an arbitrary distance from the last?

I mean, not like a trig function where each intersect is the same distance from the last. (2,0); (4,0); (6,0); (8,0). And not like a spiral where the distance gets bigger and bigger (or smaller) (2,0); (4,0); (8,0); (16,0);

But for example, some curve which intersects x-axis at (2,0); (6,0); (14,0); (15,0); (20,0); (122,0)...

Does that type function exist?

If so, is it possible to solve/get the equation, given only those intersect points?

I wouldn't need the exact equation of any particular curve. Just the equation of any curve that happens to intersect x-axis at whatever given arbitrary x values. Is that at least that possible to do?
If you specify an arbitrary finite set of points $\{a_1, a_2, a_3, \dots, a_n\}$,  the polynomial function 
$$f(x)=(x-a_1)(x-a_2)(x-a_3) \cdots (x-a_n)$$
has the desired property.
you can find the curves using matrix method by taking the columns as the x polynomials and multiply with the constant matrix which finally equated to given y. 
but on which does the degree of x which have to be taken. on what does that depend.