Find an nth degree polynomial function with real coefficients satisfying the given conditions.

Question

n=4

-1,3 and 4+3i are zeros 

f(1)=-216

f(x)=

Answer 1

Remember that the 4th root is 4-3i.

The product of the conjugate roots is x² - 8x + 25

Then (x+3)(x-3)(x² - 8x +25) = x⁴ - 10x³ + 38x² - 26x -75

The value of this function at 1 is -72; therefore, the required function is 3* the polynomial in the line above this one.