SOLUTION: I have to find the polynomial with leading coeficient 1 that satisfies the given condition: degree 4, a zero multiplicity 2 at 1, and a zero at 2+i

Question 57940: I have to find the polynomial with leading coeficient 1 that satisfies the given condition: degree 4, a zero multiplicity 2 at 1, and a zero at 2+i
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
I have to find the polynomial with leading coeficient 1 that satisfies the given condition: degree 4, a zero multiplicity 2 at 1, and a zero at 2+i
:
FOIL (x-2)(x-1) = x^2 - 3x + 2
:
x = 2 + i
x - 2 = i
(x-2)^2 = i^2, squared both sides
x^2 - 4x + 4 = -1; (i^2=-1)
x^2 - 4x + 4 + 1 = 0
x^2 - 4x + 5 = 0
:
(x^2 - 3x + 2) * (x^2 - 4x + 5) = [x^4 - 7x^3 + 19x^2 - 23x + 10]

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