Degree 4; zeros: i, -12+i , find the remaining zeros of f.

Question

Please help!!

Answer 1

You have 2 complex roots.  Complex roots come in conjugates.

 

x₁ = -i

x₂ = i

x₃ = -12 - i

x₄ = -12 + i

 

Now you have 4 roots.  We can use them to construct a 4th degree polynomial.

 

f(x) = (x² + 1)(x + [12 + i])(x + [12 - i])

 

f(x) = (x² + 1)(x² + x(12 - i) + x(12 + i) + (144 + 1))

 

f(x) = (x² + 1)(x² + 24x + 145)