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

Answer 1

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