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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

Respuesta :

HomertheGenius
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:

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 [tex]7+\sqrt{3}[/tex] and [tex]2-\sqrt{6}[/tex] 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. ' [tex]7-\sqrt{3}[/tex] ' and '  [tex]2+\sqrt{6}[/tex] ' are also roots of this polynomial equation.

Hence, option A is correct.


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