The complex conjugate root theorem states that if P is a polynomial in one variable with real coefficients, and a + bi is a root of P with a and b real numbers, then its complex conjugate a − bi is also a root of P.

This means if 2+i is zero than 2-i is also zero for P.

P has 3 zeros: 2+i, 2-i and 2-1.

Fundamental theorem of algebra says: every non-zero, single-variable, degree n polynomial with complex coefficients has, counted with multiplicity, exactly n roots

P has 3 zeros and P has degree of 2, this a contradiction with the Fundamental theorem of algebra therefore there is no such polynomial with degree 2 with zeros: 2+i and 2-1.

The complex conjugate root theorem states that if P is a polynomial in one variable with real coefficients, and a + bi is a root of P with a and b real numbers, then its complex conjugate a − bi is also a root of P.

This means if 2+i is zero than 2-i is also zero for P.

P has 3 zeros: 2+i, 2-i and 2-1.

Fundamental theorem of algebra says: every non-zero, single-variable, degree n polynomial with complex coefficients has, counted with multiplicity, exactly n roots

P has 3 zeros and P has degree of 2, this a contradiction with the Fundamental theorem of algebra therefore there is no such polynomial with degree 2 with zeros: 2+i and 2-1.