Question

Please help find values of c and b.

Answer 1

• c = 21
• b = -12

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