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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

Best Answer 

 #1
avatar+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
avatar+112827 
+1
Best Answer

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

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