Write the equation of least degree for a polynomial function that has zeros of 8 and 2 + i.

Answer 1

x = 2+i

x-2 = i

(x-2)^2 = -1

x^2-4x +4 =-1

x^2-4x+5 = 0

(x-8)(x^2-4x+5) = 0

x^3 -12x^2+37x -40 =0 is lowest degreed polynomial with the 2 zeros, if you require real coefficients

but if you allow imaginary coefficients, you can get a 2nd degree polynomial

(x-8)(x-2-i) = x^2 -(10+i)x + 16+8

Just take each zero, change its sign and stick an x in front of it, to form the factors