SOLUTION: If u and v are the roots of the equation of {{{ax^2+bx+c=0}}}, prove that {{{u^2+v^2 = (b^2-2ac)/a^2}}}.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: If u and v are the roots of the equation of {{{ax^2+bx+c=0}}}, prove that {{{u^2+v^2 = (b^2-2ac)/a^2}}}.      Log On


   

Question 1043983: If u and v are the roots of the equation of ax%5E2%2Bbx%2Bc=0, prove that u%5E2%2Bv%5E2+=+%28b%5E2-2ac%29%2Fa%5E2.
Answer by Timnewman(323) About Me  (Show Source):
You can put this solution on YOUR website!
If u and v are the roots of the equation of ax%5E2%2Bbx%2Bc=0, prove that u%5E2%2Bv%5E2+=+%28b%5E2-2ac%29%2Fa%5E2.
Solution
sum root=u+v=b/a
product root=uv=c/a
%28u%2Bv%29%5E2=b%5E2%2Fa%5E2
u%5E2%2Bv%5E2=b%5E2%2Fa%5E2-2uv
but uv=c/a
then
u%5E2%2Bv%5E2=b%5E2%2Fa%5E2-2%2Ac%2Fa
take the l.c.m and get
u%5E2%2Bv%5E2+=+%28b%5E2-2ac%29%2Fa%5E2