Prove the sum and product of roots for ax² + bx + c = 0

[rhule009]

Prove that the sum of the roots and product of the roots of the equation
ax^2 + bx + c = 0 are
-b/a and c/a respectively
thank you

 

[Werg22]

Do you know what the quadratic formula is?

 

[matt grime]

You don't need that. You dont' need to know what the roots are at all. You can let them be r and s, and just use standard results such as if r is a root of f(x), then f(x) = (x-r)g(x) for some g(x). I.e. just factorize the equation.

 

[HallsofIvy]

If u and v are roots of that equation then
[tex]ax^2+ bx+ c= a(x- u)(x- v)[/itex]<br /> Multiply the right side and compare corresponding coefficients.[/tex]