Question

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

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

Answer:

option: A

Step-by-step explanation:

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

we are given that $7+\sqrt{3}$ and $2-\sqrt{6}$ 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. ' $7-\sqrt{3}$ ' and '  $2+\sqrt{6}$ ' are also roots of this polynomial equation.

Hence, option A is correct.