# justifying solutions of an equation

• Nov 15th 2011, 12:31 AM
boromir
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?
• Nov 15th 2011, 01:16 AM
mr fantastic
Re: justifying solutions of an equation
Quote:

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.
• Nov 15th 2011, 04:53 AM
HallsofIvy
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\$"!
• Nov 15th 2011, 06:32 AM
boromir
Re: justifying solutions of an equation
Quote:

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.
• Nov 15th 2011, 01:22 PM
mr fantastic
Re: justifying solutions of an equation
Quote:

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.