Question
write a fourth degree polynomial function a leading coefficient o 1 given three of its zeros are -1, 3 and 2i, then re-write it in simplified form.
Answers
Reiny
The key concept here is that imaginary numbers always appear as conjugates
so if 2i is a zero, so is -2a
so we would have x = ±2i
x^2 = 4i^2
x^2 = -4
so x^2 + 4 is a factor
the polynomial is
f(x) = (x+1)(x-3)(x^2 + 4)
I will leave it up to you to expand it, but I would consider the factored form more simplified than the expanded form.
so if 2i is a zero, so is -2a
so we would have x = ±2i
x^2 = 4i^2
x^2 = -4
so x^2 + 4 is a factor
the polynomial is
f(x) = (x+1)(x-3)(x^2 + 4)
I will leave it up to you to expand it, but I would consider the factored form more simplified than the expanded form.