Question

A quartic polynomial P(x) has rational coefficients. If √7 and 6+i are roots of P(x)=0, what is one additional root?

Answer 1

Answer:

6-i is one additional root of P(x)=0

Step-by-step explanation:

It is given that P(x) is a quartic polynomial and P(x) has rational coefficients.

Quartic polynomial is a 4th degree polynomial.

According to the complex conjugate root theorem, if a+ib is a root of a polynomial, then a-ib is also a root of that polynomial.

$\sqrt{7}$ and 6+i are roots of the equation P(x)=0.

Here, 6+i is a complex root of P(x)=0.

Using complex conjugate root theorem, we can say that 6-i is also a root of P(x)=0.

Therefore, 6-i is one additional root of P(x)=0.