SOLUTION: for the following, find the function P defined by a polynomial of degree 3 with real coefficients that satisfy the given condition. two of the zeros are 4 and 1+i the leading

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: for the following, find the function P defined by a polynomial of degree 3 with real coefficients that satisfy the given condition. two of the zeros are 4 and 1+i the leading      Log On


   

Question 623808: for the following, find the function P defined by a polynomial of degree 3 with real coefficients that satisfy the given condition.
two of the zeros are 4 and 1+i
the leading coefficient is -5
p(x)=???
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,  

P(x) = -5(x-4)(x -(1+i))(x-(1-i)) = -5(x-4)(x^2 -2x + 2)= -5(x^3 - 6x^2 + 10x -8)

(x -(1+i))(x-(1-i)) = x^2 -2x + 2

F	First terms  x^2

O	Outside terms -x - i

I	Inside terms  -x + i

L	Last terms  (1+i))((1-i) = 2