Question

Let α and β be the roots of 3x2+4x+9=0. Then (1+α)(1+β) can be expressed in the form ab, where a and b are coprime positive integers. Find a+b.

Answer 1

since the roots are
-2/3 ±√23/3 i

1+α = 1/3 + √23/3 i
1+β = 1/3 - √23/3 i

(1+α)(1+β) = 1/9 + 23/9 = 24/9 = 8/3