Find a third-degree polynomial equation with rational coefficients that has roots –4 and 6 + i. a.)x3 – 8x2 – 11x + 148 = 0
b.)x3 – 8x2 – 12x + 37 = 0
c.)x3 – 12x2 + 37x = 0
d.)x3 – 8x2 – 11x = 0

Question

Find a third-degree polynomial equation with rational coefficients that has roots –4 and 6 + i.  a.)x3 – 8x2 – 11x + 148 = 0
b.)x3 – 8x2 – 12x + 37 = 0
c.)x3 – 12x2 + 37x = 0
d.)x3 – 8x2 – 11x = 0

anonymous · Answer

start with $(x+4)(x-(6+i))(x-(6-i)$ and multiply out 
it is not as hard as it looks since $(6+i)(6-i)=6^2+1^2=37$ and $4\times 37=148$ so you only have one real choice