+0  
 
0
207
1
avatar

The polynomial equation x^3 + bx + c = 0 where b and c are rational numbers, has 1 + sqrt(2) as a root. It also has an integer root. What is it?

 Jun 5, 2022
 #1
avatar+118587 
+1

(x-(1+sqrt2))(x-(1-sqr2)(x+a)

 

\((x-(1+\sqrt2))(x-(1-\sqrt2)(x+a)=0\\ (x-1-\sqrt2)(x-1+\sqrt2)(x+a)=0\\ ((x-1)^2-2))(x+a)=0\\ (x^2-2x-1)(x+a)=0\\ \)

 

 

Yoou can check and finish it.

 Jun 6, 2022

5 Online Users

avatar
avatar
avatar
avatar