Thread: polynomial function with 3 zeros

1. polynomial function with 3 zeros

i have a problem that states to find and simplify the polynomial function that has zeros of -3, 0, and 2i.

my current work:

f(x)=x(x+3)(x-2i)
f(x)=(x^2 + 3x)(x-2i)
f(x)=x^3 - 2ix^2 +3x^2 - 6xi

Just wanting to see if I am doing this problem in the correct way.

i have a problem that states to find and simplify the polynomial function that has zeros of -3, 0, and 2i.

my current work:

f(x)=x(x+3)(x-2i)
f(x)=(x^2 + 3x)(x-2i)
f(x)=x^3 - 2ix^2 +3x^2 - 6xi

Just wanting to see if I am doing this problem in the correct way.
$\displaystyle = x^3 + (3 - 2i) x^2 - 6i x$.

3. Does your problem forbid your function from having additional zeros? If it does no then you could try the function:

f(x)=x(x+3)(x-2i)(x+2i)

So

$\displaystyle f(x)=(x^3 - 2ix^2 +3x^2 - 6xi)(x+2i)$
$\displaystyle f(x)=(x^4 - 2ix^3 +3x^3 - 6ix^2+2ix^3 + 4x^2 +6ix^2 + 12x)$
$\displaystyle f(x)=(x^4 +3x^3+ 4x^2 + 12x)$

The advantage of this expression being that the coefficients are all real and it has all of the required zeros.