document.write( "Question 1156969: The polynomial equation $\"x%5E3+%2B+bx+%2B+c+=+0\"$ ,where b and c are rational numbers, has $\"5-sqrt%28+2+%29\"$ as a root. It also has an integer root. What is it? \n" ); document.write( "

Algebra.Com's Answer #779747 by greenestamps(13203) $\"\"$ $\"About$

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\n" ); document.write( "In a polynomial $\"ax%5E3%2Bbx%5E2%2Bcx%2Bd\"$ , the sum of the roots is -b/a.

\n" ); document.write( "In the polynomial in this problem, there is no x^2 term (i.e., it is 0x^2), so the sum of the roots is 0.

\n" ); document.write( "Given that the polynomial is rational and one root is $\"5-sqrt%282%29\"$ , another root is $\"5%2Bsqrt%282%29\"$ .

\n" ); document.write( "The sum of those two roots is 10, so the third root is -10.

\n" ); document.write( "ANSWER: -10

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