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Help is appreciated

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The polynomial equation $x^3 + bx + c = 0,$where $b$ and $c$ are rational numbers, has $3-\sqrt{7}$ as a root. It also has an integer root. What is it?

Jan 12, 2021

#1
+112827
+1

Roots come in pairs

So if one root is   3- sqtr 7   another is   3+ sqrt 7

Expand

$$[x-(3-\sqrt7)]\;[x-(3+\sqrt7)]$$

Divide  the question cubic polynomial by the answer.

Now think about what you have found.

Jan 12, 2021

#1
+112827
+1

Roots come in pairs

So if one root is   3- sqtr 7   another is   3+ sqrt 7

Expand

$$[x-(3-\sqrt7)]\;[x-(3+\sqrt7)]$$

Divide  the question cubic polynomial by the answer.

Now think about what you have found.

Melody Jan 12, 2021