SOLUTION: Hello! On my math homework I am struggling deeply on a problem, "Write an equation of a quintic polynomial with roots 1, -2, 3, and i (imaginary, not a variable) with a y-intercep

Question 839332: Hello! On my math homework I am struggling deeply on a problem,
"Write an equation of a quintic polynomial with roots 1, -2, 3, and i (imaginary, not a variable) with a y-intercept of 18"
I am very lost on this, as I have tried several times and cannot find a solution.
Thanks!
Found 2 solutions by josgarithmetic, ankor@dixie-net.com:
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
The binomial factors needed are (x-1), (x+2), (x-3), (x-i), and (x+i).

The function, being 18 when x=0, would take the form and you want to solve for k.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
"Write an equation of a quintic polynomial with roots 1, -2, 3, and i (imaginary, not a variable) with a y-intercept of 18"
:
The factors derived from the above: (x-1)(x+2)(x-3)(x^2+1)
FOIL (x-1)(x+2) = x^2 + x - 2
then
(x-3)*(x^2 + x - 2) = x^3 - 2x^2 - 5x + 6
then
(x^2+1)*(x^3-2x^2-5x+6) = x^5 - 2x^4 - 4x^3 + 4x^2 - 5x + 6
To get a y intercept of 18 multiply eq by 3
3x^5 - 6x^4 - 12x^3 + 12x^2 - 15x + 18 is polynomial
:
Looks like this

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