Write a function with the given characteristics? (details inside)

Question

anonymous · Answer

A polynomial with rational coefficients having roots 3, 3, and 3-i

anonymous · Answer

does this mean 3 is a root twice?

anonymous · Answer

$$(x-3)^2(x-(3+i))(x-(3-i))$$

anonymous · Answer

yes, and i'm confused because i need to find the original equation (for example, something like x^3 + x^2 + x + k)

anonymous · Answer

Just multiply the factors that satellite73 gave in is response above.

anonymous · Answer

but then won't i end up with 3i as part of the polynomial?

anonymous · Answer

1. multiply (x-3)*(x-3)
you should get: (x^2-6x+9) - ans
2. multiply (x-3-i)(x-3+i)
You should get: x^2 - 3x +ix-3x+9-3i-ix+3i-i^2 (remember i^2 = -1)
NOTE: ix and -ix cancels, -3i and 3i cancels.
You should have left: (x^2-6x+10) - ans

3. multiply the ans in part1 by the answer in part2
(x^2-6x+9)(x^2-6x+10)=(x^4-6x^3+10x^2-6x^3+36x^2-60x+9x^2-54x+90)
                                =(x^4-12x^3+55x^2-114x+90) (simplify by combining like terms)

Answer: (x^4-12x^3+55x^2-114x+90)

anonymous · Answer

Thank you so much!