Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing​ utility, use it to graph the functi

Question

n=4

-1,4,4+4i are zeros

f(1)=-150

Answer 1

Since f(x) has real coefficients, complex roots occur in conjugate pairs.  So, since 4+4i is a root, so is 4-4i.

 

f(x) = A(x-(-1))(x-4)(x-(4+4i))(x-(4-4i))

 

       = A(x+1)(x-4)[(x-4)-4i][(x-4)+4i]

 

       = A(x²-3x-4)[(x-4)²+16]

 

       = A(x²-3x-4)(x²-8x+32)

 

Since f(1) = -150, we have A(-6)(25) = -150

 

                                                 A = 1

 

f(x) = (x²-3x-4)(x²-8x+32)

 

You can multiply it out, if necessary.