Find a third degree polynomial function with REAL coefficien

Find a third degree polynomial function with REAL coefficients that includes among its zeroes –6 and 2i

Solution

REAL coefficients => as 2i is the zero ,its conjugate -2i is also the zero

third degree polynomial function with zeroes -6 , 2i , -2i is

p(x)=(x-(-6))(x-2i)(x-(-2i))

p(x)=(x+6)(x²-(2i)²)

p(x)=(x+6)(x²-(-4))

p(x)=(x+6)(x²+4)

p(x)=x³+6x²+4x +24

third degree polynomial function with REAL coefficients is x³+6x²+4x +24