Roots & Product of ax^2 + bx + c = 0

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The discussion focuses on proving that for the quadratic equation ax^2 + bx + c = 0, the sum of the roots is -b/a and the product of the roots is c/a. Participants emphasize that knowledge of the quadratic formula is unnecessary for this proof. Instead, they suggest using the factorization method, where the equation can be expressed as a(x - u)(x - v), allowing for the comparison of coefficients to derive the required relationships.

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rhule009
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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
 
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Do you know what the quadratic formula is?
 
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.
 
If u and v are roots of that equation then
ax^2+ bx+ c= a(x- u)(x- v)[/itex]<br /> Multiply the right side and compare corresponding coefficients.
 

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