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

Question

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

campbell_st · Answer

well it will have a conjugate pair for 3 - i

the polynomial will be

P(x) = (x -3)(x -3)(x -(3 -i))(x +(3 - i))

just distribute for the answer

cookiimonster627 · Answer

would it be( x-3^2)(x-(3-i))(x+(3-i)? @campbell_st

campbell_st · Answer

well complex solutions 

x = 3 - i

subtract 3 from both sides 

(x - 3) = -i

now square both sides 

$$(x - 3)^2 = (-i)^2$$

and knowing i^2 = -1  you get 

$$x^2 - 6x + 9 = -1$$

so the equadraict fractor is 

$$x^2 - 6x + 10 = 0$$

and knowing the rational zeros you can say 

$$P(x) = (x - 3)(x -3)(x^2 - 6x + 10)$$

cookiimonster627 · Answer

I got x^4-12x^3+55x^2-114x+90 
would that be right or wrong? @campbell_st