SOLUTION: Can you please help me solve this problem? Find a polynomial function of lowest degree with rational coefficients and -3 and 4i as some of its zeros. a)f(x)= x^2+3x-4xi-12i

Question 433961: Can you please help me solve this problem?
Find a polynomial function of lowest degree with rational coefficients and -3 and 4i as some of its zeros.
a)f(x)= x^2+3x-4xi-12i
b)f(x)= x^3+3x^2-16x-48
c)f(x)= x^3-3x^2+16x-48
d)f(x)= x^3+3x^2+16x+48
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
If 4i is a zero, then so is -4i.
The constant term is equal to -(-3)(4i)(-4i) = -48i*i = 48.
The coefficient of x is (-3)(4i) + (-3)(-4i) + (4i)(-4i) = -16i*i = 16
The coefficient of x^2 is -(-3 + 4i + (-4i)) = 3
Therefore the answer is letter d.
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