Thread: sum and product of roots

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.

Originally Posted by Duke

The book used identities to show if x , y are the roots of the equation az^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.

The roots of are the roots of (of course ).

But by the factor theorem

Hello, Duke!

Your use of and is confusing.
I'll modify it to "standard" notation.

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Good thinking!

Yes, you are correct.

Those roots/coefficients relations are usually given
. . (or should be given) with an "if and only if".

Thanks for both helpful replies.