I need some help to solving a quadratic

runddansm88e

runddansm88e

Answered question

2022-04-08

I need some help to solving a quadratic equation, but translating it into Dedekind Cuts and using the completing the square way. I first solved the equation in a usual way so i can know where do i have to get, but the Dedekind Cut stuff, I don't know how to use it on it.
Given: x2+6x+3=0

Answer & Explanation

xxkrnjangxxed9q

xxkrnjangxxed9q

Beginner2022-04-09Added 14 answers

You can notice that one of the roots is less than -3 and other one is greater than -3 and the sign of x2+6x+3 is negative between these roots. So for the greater root use
A={xxQ,x3,x2+6x+3<0}{xxQ,x3}
And for the other root use
B={xxQ,x<3,x2+6x+3>0}
Confirm that both these sets satisfy the following defining properties of a Dedekind cut
- each is a non-empty proper subset of Q
- if a rational number belongs to the set, all the smaller rationals also belong to the set
- the set has no maximum member ie given any member of the set we can find another member which is greater than the given member
And then you need to show further that these sets A,B indeed satisfy the equation x2+6x+3=0. This will require you to know how to multiply and add Dedekind cuts. This part of the exercise is boring and lengthy.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?