Polynomial Function

Question

Find a polynomial of least degree having only real coefficients, a leading coefficient of one, and zeros of 2 and 2+i

Answer 1

To ensure real coefficients, the complex conjugate of a complex zero must also be a zero. Therefore, the minimum set of zeros is

2

2 + i

2 - i

and the polynomial is

p(x) = A(x - 2) [x - (2 + i)] [x - (2 - i)],

where A ≠ 0.

A is the leading coefficient, so A = 1 (given).

p(x) = (x - 2) [x - (2 + i)] [x - (2 - i)]

Now multiply this through and simplify, and get your polynomial. The coefficients will all come out real.