SOLUTION: If the roots are ax^2+bx+c=0, differ by 1, show that they are (a-b)/2a and -(a+b)/2a, and prove that b^2=a(a+4c)

Question 1132708: If the roots are ax^2+bx+c=0, differ by 1, show that they are (a-b)/2a and -(a+b)/2a, and prove that b^2=a(a+4c)
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!
If the roots are ax^2+bx+c=0, differ by 1,

Let the roots be r and r+1

 and 

So 


 








   <-- that's one root

The other root is r+1, so we add 1 to both sides:







  <-- that's the other root

and prove that b^2=a(a+4c)

Substitute either root in the original.  I'll use

, since it has only one - sign. 



 





Multiply through by 4a













Edwin

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