I have just been reading about the relationship between the roots of a quadractic and the coefficents.

The book used identities to show if x , y are the roots of the equation aqz^2+bz+c=0, then -b/a=x+y and c/a=xy. Then it asked me to find the equation with roots whose sum and product were known.

I was doing the questions but I was thinking surely something else needs to be true. Am I correct in saying in order to do this question, you need to know that the converse is true as well. I.E. If x+y =-b/a and xy=c/a, then x,y are the roots of the equation. This can be seen by solving the relations simultaneously and finding that the only 2 x,y satisfying the relations are the two roots of the quadractic equation.

Thanks for reading and answering.