Question

A polynomial has one root that equals 2+i.Name one other root of this polynomial.

Answer 1

2-i. Complex roots always come in pairs (complex conjugates)

Answer 2

ANSWER

One other root of this polynomial is
$2 - i$


EXPLANATION


One property of the complex root of a polynomial is the conjugate root property.


If one root of a polynomial is
$a + bi$
then the conjugate is also a root of this polynomial.

The conjugate of
$a + bi$
is
$a - bi$

Also the conjugate of
$a - bi$

is
$a + bi$



Therefore if
$2 - i$
is a root of the polynomial, then its complex conjugate
$2 + i$
is also a root of that polynomial.

The same applies to purely imaginary complex roots too.

Thus, if
$bi$
is a root then its conjugate
$- bi$
is also a root.