Find an nth-degree polynomial function n =4: -4 6. and 2 + 3i are zeros Question 8, 9.5.15 real coefficients, a leading coefficient of 1, and satisfying the given conditions.

Question

Find an nth-degree polynomial function with real coefficient of 1, and satisfying the given conditions.

n =4; -4, 6, and 2 + 3i are zeros

f(x)=

Answer 1

x+4=0

x-6=0

(x+4)(x-6)=0

x^2-2x -24=0

x=2+3i

x-2=3i

x^2-4x +4= -9

x^2 -4x +13=0

(f(x)= (x^2-4x +13)(x^2-2x-24)=0

f(x)= x^4 -6x^3 -19x^2 +70x - 372