3x^2 + 11x - 4 = 0
Look for two factors of -12 that add up to 11 -> -1 and 12
(3x - 1)(x + 4) = 0
x = 1/3 or -4
So the answer you want is D
An easy way to answer questions like this is simply to try each option until one works.
3 x 0^2 + 11 x 0 = 0 so not A
3 x (-11/3)^2 + 11 x -11/3 = 0 so not B
3 x 4^2 + 11 x 4 = 92 so not C
3 x (1/3)^2 + 1 x 1/3 = 12/3 = 4 correct
I doubt E would be marked correct but in fact A and E are opposite statements so one of them must be true