Question

Find the polynomial.

Answer 1

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