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Find a polynomial of degree 4 that has √2 + √7 as a root. That is, find integers a,b,c,d,e, so that x = √2 + √7 is a solution to the equation

 ax^4+bx^3+cx^2+dx+e=0.

 

1. Find all the roots of this polynomial.

2. Given two distinct positive integers x and y, what can you conclude about polynomials that have \(\sqrt{x}+\sqrt{y}\) as a root.

 

Please explain answers.

Melody, Cphill, EP??

 Feb 27, 2020
edited by RandomUser  Feb 27, 2020
edited by RandomUser  Feb 27, 2020
 #1
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How about the following:

 

I'll leave you to think about part 2.

 Feb 27, 2020

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