For this case we have the following polynomial roots:
x = -1 / 3
x = 4
Let's assume that the correct polynomial is:
3x2 - 11x - 4 = 0
We evaluate the roots in the polynomial
For x = -1 / 3:
3 (-1/3) ^ 2 - 11 (-1/3) - 4 = 0
3 (1/9) - 11 (-1/3) - 4 = 0
1/3 + 11/3 - 4 = 0
12/3 - 4 = 0
4 - 4 = 0
We observe that x = -1 / 3 is a root.
For x = 4:
3 (4) ^ 2 - 11 (4) - 4 = 0
3 (16) - 44 - 4 = 0
48 - 48 = 0
We observe that x = 4 is a root.
Answer:
3x2 - 11x - 4 = 0