Need help -Math Finale-

Question

Find a polynomial of degree 4 With integer coefficients search that -1 is a zero, 2 is a zero and 4+i is a zero

Answer 1

The complex conjugate of a complex zero must also be a zero, so the 4 zeros are

-1

2

4 + i

4 - i

f(x) = A(x + 1)(x -2) [x - (4 + i)] [x - (4 - i)],

where A is a real integer and A ≠ 0. Expand to standard form if you wish. The coefficients will all come out real and integer.