# Thread: justifying solutions of an equation

1. ## justifying solutions of an equation

If I wrote $\displaystyle ax^2+bx+c=0$ --> x= d,e for example, then am I right in thinking that all this says is that d and e are the only possible solutions and that I would need 'iff' to justify that these are the solutions?

2. ## Re: justifying solutions of an equation

Originally Posted by boromir
If I wrote $\displaystyle ax^2+bx+c=0$ --> x= d,e for example, then am I right in thinking that all this says is that d and e are the only possible solutions and that I would need 'iff' to justify that these are the solutions?
If you are asked to solve an equation, you solve it! Solving it means finding all the values of, in this case, x that satisfy the equation. 'iff' is irrelevant.

3. ## Re: justifying solutions of an equation

Although, if I were your teacher, I would expect more than just "$\displaystyle ax^2+ bx+ c= 0---> x= d, e"$ to indicate that d and e are meant to be the solutions. If you want to really shock your teacher, try writing full sentences: "x= d and x= e are the solutions to the equation $\displaystyle ax^2+ bx+ c= 0$"!

4. ## Re: justifying solutions of an equation

Originally Posted by mr fantastic
If you are asked to solve an equation, you solve it! Solving it means finding all the values of, in this case, x that satisfy the equation. 'iff' is irrelevant.
Yes, and one would of course achieve full marks but the reasoning would be faulty.

5. ## Re: justifying solutions of an equation

Originally Posted by boromir
Yes, and one would of course achieve full marks but the reasoning would be faulty.
I have absolutely no idea on what basis you make the above comment.