Find the polynomial function the set of zeros below. Assume a stretch factor of a = 1.

Question

2, - 1 - √7i, - 1 + √7i

Answer 1

f(x) = (x-2)[x-(-1-√7i)][x-(-1+√7i)]

 

      = (x-2)[(x+1)+√7i][(x+1)-√7i]

 

      = (x-2)[(x+1)²-(√7i)²]

 

      = (x-2)(x²+2x+1+7)

 

      = (x-2)(x²+2x+8)  = x(x²+2x+8) - 2(x²+2x+8)

 

                                = x³+2x²+8x-2x²-4x-16

 

                                = x³+4x-16