How to establish the connection between the zero point of function and the root of equation?

The function f (x) = 0,
The root X of the equation f (x) = 0
e.g.,
f(x)=ax+b=0 ==>x=-b/x
f(x)=ax*x+bx+c=0 ==>
x=[-b±(b^2-4ac)^(1/2)]/2a
f(x)=asin(x)+b=0 ==> x=arcsin(-b/a)

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