Question

explain why the facts given are contradictory.

$f\left(x\right)$is a polynomial function of degree 3 whose coefficients are real numbers; its zeros are 4 + i, 4 - i, and 2 + i.

Short answer

The degree of polynomial is 4 and not 3

Step-by-step solution

Given information

We are given a statement f(x) is a polynomial function of degree 3 whose coefficients are real numbers; its zeros are 4 + i, 4 - i, and 2 + i.

Explanation

We are given that 3+i is a root of the polynomial hence by conjugate property 3-i is also a root of the polynomial. hence we have 4 roots of the polynomial hence the degree of polynomials is 4 and not 3