Question

Because 1+2i is a zero of f(x)=x^(2)-2x+5, we can conclude that 1-2i is also a zero

Answer 1

Complex conjugate pairs are always roots of a polynomial with real coefficients.

Step-by-step explanation:

Given that 1 + 2i is a zero of the function f(x) = x^2 - 2x + 5, we can conclude that 1 - 2i is also a zero.

This is because complex conjugate pairs are always roots of a polynomial with real coefficients. In other words, if a + bi is a root of a polynomial, then a - bi is also a root.

Since the given polynomial f(x) = x^2 - 2x + 5 has real coefficients, the complex conjugate of 1 + 2i, which is 1 - 2i, is also a root of the polynomial.