To find the other root of the quadratic equation, we need to use the properties of an arithmetic progression (A.P.) and the fact that one root is given as 2.

Let's assume that the common difference of the A.P. is d.

Given: a, b, c are in A.P.
This implies that b - a = c - b = d.

Let's consider the quadratic equation ax^2 + bx + c = 0.
Since one root is given as 2, we can substitute x = 2 into the equation.

This gives us:
a(2)^2 + b(2) + c = 0
4a + 2b + c = 0 ----(1)

Now, let's find the other root of the quadratic equation.

Using the quadratic formula, the roots of the equation ax^2 + bx + c = 0 can be found as:
x = (-b ± √(b^2 - 4ac))/(2a)

Since one root is given as 2, let's substitute x = 2 into the quadratic formula and simplify.

2 = (-b ± √(b^2 - 4ac))/(2a)
2a = -b ± √(b^2 - 4ac)
4a^2 = b^2 - 4ac
4a^2 - b^2 = -4ac
b^2 - 4a^2 = 4ac
(b + 2a)(b - 2a) = 4ac

From equation (1), we have 4a + 2b + c = 0.
We can express c in terms of a and b as:
c = -4a - 2b

Similarly, we can express c in terms of a and b using the equation (b + 2a)(b - 2a) = 4ac:
c = (b + 2a)(b - 2a)/(4a)

Now, substitute the value of c in equation (1) with the above expression for c:
4a + 2b + (b + 2a)(b - 2a)/(4a) = 0

Simplifying the equation further, we get:
16a^2 + 8ab + (b + 2a)(b - 2a) = 0

Expanding the expression, we have:
16a^2 + 8ab + (b^2 - 4a^2) = 0
16a^2 + 8ab + b^2 - 4a^2 = 0
12a^2 + 8ab + b^2 = 0
(2a + b)^2 = 0

Taking the square root of both sides, we get:
2a + b = 0

Substituting this value in the expression for c, we have:
c = -4a - 2b
c = -4a - 2(-2a)
c = -4a + 4a
c = 0

Hence, the quadratic equation ax^2 + bx + c = 0 with roots 2 and -1.25 is satisfied when c = 0.