Processing math: 100%
 
+0  
 
0
675
3
avatar

Find the sum of the squares of the roots of 3x^2 + 4x + 12 = 0.

 Mar 19, 2020
 #1
avatar+4625 
+1

We are asked to find: x2+y2, for x and y are the roots of the equation.

3x2+4x+12 has a sum of 43.

3x2+4x+12 has a product of 123=4.

 

Use the manipulation:(x+y)22(xy)=x2+y2.

 

Thus, the answer is (43)22(4)=169729=569.

 Mar 19, 2020
 #2
avatar+130477 
+2

By Vieta....

 

We have  the form   Ax^2 + Bx + C  = 0

 

Let the roots  be  R1 and R2

 

The sum of these  =  -B/A  =   -4/3  =   R1 + R2     (1)

 

And the product of these =  C/A  =   =  12/3 =  4  = R1*R2  which implies that  8 = 2*R1*R2

 

Square  (1)  and we get that

 

R1^2  + 2*R1*R2  + R2^2  =  16/9

 

R1^2  + 8  + R2^2  =  16/9

 

R1^2  + 72/9  + R2^2  = 16/9      subtract 72/9  from both sides

 

R1^2 + R2^2  =  16/9 - 72/9  =  -56/9

 

 

cool cool cool

 Mar 19, 2020
 #3
avatar
0

THX SO MUCH GUYS!!!!!!

 Mar 19, 2020

0 Online Users