ccooley wrote:
No. If you have the roots, you have the quadratic equation. Think about it like this: if you know the roots, you can immediately calculate the equation itself, by multiplying out (x-a)(x-b) = 0. Could you create two different equations using the same pair of roots? No, because there's just one, single, clear process for going from roots -> equation.
However, technically, it depends on which quadratic equations you consider to be different. For example, the equations x^2 + 2x + 1 = 0 and 2x^2 + 4x + 2 = 0 have the exact same root. In my eyes, though, those are the 'same' quadratic equation - one of them simplifies directly into the other, so they're mathematically identical.
So a DS question asks us to find a quadriatic equation and one of the statement gives us the roots of the equation,is that particular statement sufficient? (Is there any
OG questions of this format? I haven't gone through all the OGs yet.)
ccooley wrote:
To RaghavSingla's comment above: try actually drawing two different parabolas using those criteria. (Remember that a parabola has to be symmetrical left-right!). You'll find that it's harder than you'd think... you can come up with parabolas that look different, but mathematically, they're actually just multiples of each other.
What about two parabolas who are the inverse to each other in terms of sign(x^2+2x+1 and -x^2-2x-1). These clearly have the same pair of roots but are different parabolas.