Web Analytics
malo8vemmather
Answered

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

A7 - sqrt 3 , 2 + sqrt 6
B3 - sqrt 7 , 6 + sqrt 2
C7 + sqrt 3 , 2 - sqrt 6
D3 + sqrt 7 , 6 - sqrt 2

Verified Answer :

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 \(7+\sqrt{3}\) 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.


Related Questions