determine the values of n in each equations that 1 root is triple the other root 3x^2-4x+n=0

Since one root is triple the other, we assume  x1 and 3x1
are the roots of the given equation 3x^2-4x+n = 0.

Then
3x^2 -4x+n = k(x-x1)(x-3x1)^2 should be an identity. So we choose k = 3 to make the
coefficient of x^2 equal on both sides.

3x^2-4x +n =
3(x-x1)(x-3x1)

We expand the right
side.

3x^2-4x+n = 3x^2- 3(x1+3x1)x
+9x1^2

Equating the coefficients of x's on both sides, we
get:

-4 = -(x1+3x1).

4x1 =
4

x1 = 1

Equating the constant
terms, we get:

n = 9x1^2 .

 n
= 9*1^2.

n = 9