I want to find the first positive and first negative root of a bessel function

j2 := (x, a) -> k(x)^2*a^2*(diff((diff(1000000000*sin(1/1000000000*k(x)*a)/(k(x)*a), x))/(k(x)*a), x))/(k(x)*a)

I couldn't use the built in bessel function with two variables, so I had to enter it by hand.

I want to find the values of x where j2 is zero as a function of a:

f := (a) -> RootOf(j2(x, a), x, 0 .. 2)

plot(f(a), a = 2 .. 2.25, y = -3 .. 3)