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Mathematics 40 Online
OpenStudy (anonymous):

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

OpenStudy (anonymous):

If the coefficients are rational, then those irrational roots have to come in conjugate pairs.

OpenStudy (anonymous):

ummm , i have no idea what you mean by that ? lol

OpenStudy (anonymous):

Ok, that's fine. Let's go over some vocabulary then. The square root of a number that is not a perfect square is irrational. 7+√3 and 2-√6 are irrational.

OpenStudy (anonymous):

If the polynomial has rational coefficients, then those irrational numbers have to cancel out. That's why you need a conjugate (a number that has the opposite of what you're trying to cancel).

OpenStudy (anonymous):

ok , i see . . .

OpenStudy (anonymous):

e.g. the conjugate of 1+√2 is 1-√2. The +√2 and -√2 will cancel out to give rational coefficients.

OpenStudy (anonymous):

yesss . .

OpenStudy (anonymous):

So, of those choices, which contains the conjugates of 7+√3 and 2-√6? Look carefully, because they are all pretty similar-looking.

OpenStudy (anonymous):

b ?

OpenStudy (anonymous):

or c ?

OpenStudy (anonymous):

Neither of those.

OpenStudy (anonymous):

:( i feel slow . . . . lol

OpenStudy (anonymous):

well then i have to say d now ?

OpenStudy (anonymous):

Hmm, you might be misunderstanding what I mean by "opposite" "Opposite means the + or - signs are switched.

OpenStudy (anonymous):

+3 is the opposite of -3, etc.

OpenStudy (anonymous):

oh , i guess i did misunderstand it . it has to be a then .

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