Answer:
Explanation:
You want the coefficients of the quadratic with roots (3±2i√3)/2 and a leading coefficient of 4.
Coefficients
The value b/a is the opposite of the sum of the roots.
b/a = -((3+2i√3)/2 +(3-2i√3)/2) = -(3/2 +3/2) = -3
b = -3a = -3(4)
b = -12
The value c/a is the product of the roots. This will be the difference of squares:
c/a = (3+2i√3)/2 × (3-2i√3)/2 = (3² -(2i√3)²)/4 = (9 +12)/4 = 21/4
c = a(21/4) = (4)(21/4)
c = 21