Answer:
Step-by-step explanation:
The sum of the two roots is ...
(-1 +4i) + (-1 -4i) = -2
This value is the opposite of b/2, so b = -2(-2) = 4.
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The product of the two roots is ...
(-1 +4i)(-1 -4i) = ((-1)² -(4i)²) = 1 +16 = 17
This value is c/2, so c = 2(17) = 34.
The value of b is 4; the value of c is 34.
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Further explanation
A quadratic factored as ...
y = a(x -p)(x -q)
expands to ...
y = ax^2 -a(p+q)x +apq
So, for roots p and q, ...
b = -a(p+q)
c = apq
In this problem , a=2, p=-1+4i, q=-1-4i.
