+0  
 
0
4
1
avatar+354 

Find the sum of the squares of the roots of $2x^2+4x-1=x^2-8x+3$.

 Jun 21, 2024

Best Answer 

 #1
avatar+42 
+1

If we combine like terms, we get \(x^2+12x-4\). By Vieta's, the sum of the roots is -12 and the product is -4. If the roots are a and b, then \((a+b)^2=-12^2=144\). If we subtract twice the product, we can find the sum of the squares of the roots. \(144-(-8)=152\).

 

Feel free to tell me if I did anything wrong! :D

 Jun 21, 2024
 #1
avatar+42 
+1
Best Answer

If we combine like terms, we get \(x^2+12x-4\). By Vieta's, the sum of the roots is -12 and the product is -4. If the roots are a and b, then \((a+b)^2=-12^2=144\). If we subtract twice the product, we can find the sum of the squares of the roots. \(144-(-8)=152\).

 

Feel free to tell me if I did anything wrong! :D

Tottenham10 Jun 21, 2024

8 Online Users

avatar
avatar
avatar
avatar