Find an nth degree polynomial function with real coefficient

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 function and verify the real zeros and the given function value n-3; 2 and 21 are zeros. f(-1)-15

Solution

Since the zeros of polynomials are 2 and 2i

we also know the conplex roots is always in conjugate

so the equation will be

let f(x)=a*(x-2)(x-2i)(x+2i)=a*(x-2)(x^2-4i^2)=a*(x-2)(x^2+4)=a*(x^3-2x^2+4x-8)

Also Given f(-1)=15

=> a*(-1-2-4-8)= 15

=>a= -15/15= -1

therefore f(x)= a*(x^3-2x^2+4x-8)= -1*(x^3-2x^2+4x-8)= -x^3+2x^2-4x+8 .............Ans