Suppose 3/4 is a root of a polynomial equation. what does this tell us about the leading coefficient and the constant term in the equation

Nothing new about leading coefficient. Definition says it can't be zero. It can always be made equal to one by dividing through.

Constant term cannot be zero unless a root is zero.

Step-by-step explanation:

x-3/4 = 0 has root 3/4 constant term - 3/4

(x-3/4) (x-b) = 0 has roots 3/4 and b, constant term 3b/4 which is zero only if b is zero.

(x-3/4) (x-b) (x-c) = 0 has roots 3/4, b, c, constant term - 3bc/4 which is zero only if b or c is zero.

Etc ...