Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

3, -13, and 5 + 4i

Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

3, -13, and 5 + 4i

triciaal · Answer

if 3 is a zero of the function then x-3 is a factor etc 
suggest expanding this to get the function   I am not sure of the last factor but I used to conjugate of the complex factor given 
remember i^2 = -1
(x-3(x + 13)( x-5-4 i)(x +5 + 4 i)

anonymous · Answer

f(x) = x4 - 8x3 - 12x2 + 400x - 1599 

 f(x) = x4 - 200x2 + 800x - 1599 

 f(x) = x4 - 98x2 + 800x - 1599 

 f(x) = x4 - 8x3 + 12x2 - 400x + 1599