Question

A polynomial equation with rational coefficients has the roots 7 + *sqrt* 3 , 2 - *sqrt* 6. Find two additional roots.

a. 7 - *sqrt* 3 , 2 + *sqrt* 6
b. 3 - *sqrt* 7 , 6 + *sqrt* 2
c. 7 + *sqrt* 3 , 2 - *sqrt* 6
d. 3 + *sqrt* 7 , 6 - *sqrt* 2

Answer 1

If the coefficients of a polynomial equation are rational, then the irrational roots have to come in conjugate pairs.
The conjugate of 7 +√ 3 is 7 - √ 3 and the conjugate of 2 - √ 6 is 2 + √ 6.
Answer:
A ) 7 - √ 3 , 2 + √ 6

Answer 2

option: A

Explanation:

" if for a polynomial with rational coefficients has irrational roots then these irrational roots will always appear in pair " .

we are given that
`7+√(3)` and
`2-√(6)` are two roots of a polynomial equation with rational coefficients, then it's complex conjugate is also a root of this polynomial equation i.e. '
`7-√(3)` ' and '
`2+√(6)` ' are also roots of this polynomial equation.

Hence, option A is correct.