中5級的數學題5點 - Yahoo!知識+

Method 1 :The other root is a - 2iSum of the roots :a + 2i + a - 2i = - 6/2a = - 3/2Product of the roots :(- 3/2 + 2i) (- 3/2 - 2i) = b/29/4 - (- 4) = b/2b = 25/2
Method 2 :Sub x = a+2i to the equation :2(a+2i)² + 6(a+2i) + b = 02(a² + 4ai - 4) + 6(a + 2i) + b = 0(2a² + 6a + b - 8) + (8a + 12)i = 0So2a² + 6a + b - 8 = 0.....(1)
{
8a + 12 = 0.....(2)By (2) , a = - 3/2Put it to (1) :2(- 3/2)² + 6(- 3/2) + b - 8 = 0b = 25/2