Question

Find a polynomial function with the given zeros. i, 0, 2

Answer 1

If we want to construct a polynomial with real coefficients having zeros i, 0, 2 we have to consider the conjugate of i also, since complex zeros occur only in pairs as complex conjugates. Therefore, a polynomial of the required type is a fourth degree polynomial given by p(z) = (2-i)(+i)(2 - 0) (2 – 2) It can also be written as p(x) = 2(z − 2)(2+1) Thus p(x) = 24 – 223 +22 – 22 If complex coefficients are allowed, then a polynomial of the smallest de- gree having zeros i, 0, 2 can be given as 9(2) = 2(z - i)(x - 2) That is g(x) = x2 – (2+i)2 + 2iz