Question

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

Answer 1

ANSWER

One other root of this polynomial is

`2 - i`


Step-by-step 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.

Answer 2

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