SOLUTION: The polynomial equation {{{x^3 + bx + c = 0}}},where b and c are rational numbers, has {{{5-sqrt( 2 )}}} as a root. It also has an integer root. What is it?

Question 1156969: The polynomial equation ,where b and c are rational numbers, has as a root. It also has an integer root. What is it?
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

In a polynomial , the sum of the roots is -b/a.

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.

Given that the polynomial is rational and one root is , another root is .

The sum of those two roots is 10, so the third root is -10.

ANSWER: -10

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