SOLUTION: Write a polynomial function with REAL COEFFICIENTS AND LEADING coefficient of 1 and with the given zeros: -2, 4, 3+i

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Write a polynomial function with REAL COEFFICIENTS AND LEADING coefficient of 1 and with the given zeros: -2, 4, 3+i      Log On


   

Question 927066: Write a polynomial function with REAL COEFFICIENTS AND LEADING coefficient of 1
and with the given zeros: -2, 4, 3+i
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Since the coeffcients are real, and 3+i is a solution, so is its
conjugate 3-i

Start with 

      x=-2,  x=4,     x=3+i,    x=3-i
    x+2=0, x-4=0, x-3-i=0   x-3+i=0 

Multiply all the left sides and all the right sides, which gives

  (x+2)(x-4)(x-3-i)(x-3+i) = 0

Do all that multiplying remembering that i2 = -1

and get

        x4-8x3+14x2+28x-80 = 0

So the polynomial function f(x) is

 f(x) = x4-8x3+14x2+28x-80 

Edwin