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Suppose that all four of the numbers

2-sqrt(5), 4+sqrt(10),14-2sqrt(7), -sqrt(2)

are roots of the same nonzero polynomial with rational coefficients. What is the smallest possible degree of the polynomial?

 Jul 10, 2024
 #1
avatar+867 
-1

There are four roots, so the smallest possible degree of the polynomial is 4.

 Jul 10, 2024
 #2
avatar+174 
+2

The answer is 8. 

Each of the conjugate of the roots are also roots, so we have 8. 

 Jul 11, 2024

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