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Since (x - c) is a factor substitute x = c in the equation. (Because x - c = 0 which implies x = c)

so the equation transforms to
x^2 - 11x + 4c = 0
c^2 - 11c + 4c = 0
c^2 = 7c
c = 7

Now substitute c = 7 in the equation
x^2 - 11x + 4c = 0
x^2 - 11x + 28 = 0
The roots of which are 7 and 4.
So the larger root is 7
Answer is B

BTW what is the OA?

An other way to solve the problem might be this:

Since we know that (x - c) is a factor then one root will be c (Because x - c = 0 which implies x = c)

Let the other root be "y"

Now sum of the roots is 11 and product of the roots is 4c.
=>y + c = 11 and yc = 4c
From the above equations we get y = 4 and c = 7.

So the answer is B