+0  
 
0
92
1
avatar

Let x^2+bx+c=0 be a quadratic whose roots are each two more than the roots of 3x^2-5x-17. What is c?

 Apr 23, 2022
 #1
avatar+124598 
0

Call the roots of the second quadratic  m and n

 

The product  of  these roots =   -17/3   = mn  

And the sum of the roots =  m + n  =  5/3    ⇒    2 (m + n)  =   10/3   

 

So...in the polynomial of interest    the product of the roots  =   (m + 2) (n + 2) =   c

 

So

 

mn + 2 (m + n)  +  4  =  c

 

-17/3  + 10/3  + 4 =   c

 

-7/3 + 4  = c

 

-7/3  + 12/3  =  c

 

5/3 =  c

 

 

cool cool cool

 Apr 23, 2022

36 Online Users

avatar