If 2 is the repeated equal root of a quadratic equation,

Is that common to say that the equation has two postive roots?

It is common to distinguish between unique roots.

If 2 is the repeated equal root of a quadratic equation' date='

Is that common to say that the equation has two postive roots?[/quote']

 

No you say it has one positive root.

I would say it has a postive repeated root

I do what pulkit does. If you have two positive roots of 2, I would only say that it has a root of positive two, one unique solution. If instead it were 2 and 3, than I would say it had the roots of 2 and 3.

I find that after finding the coefficients of qudra, sometimes we need to use the discriminant to ensure it again.

And sometimes we need to reject some or one of the answers.

In what case, we need do to so? I want to have this knowledge and reduce the time of doing maths.

You only reject answers when the equations you started with were not simple quadratics. In such cases you have no choice but to follow this check, accept or reject approach.

Is it common for us to restrict the range of x first?

Like,

|x|=2x+1

When x >= 0

x=2x+1

x=-1(rejected)

When x<0

-x=2x+1

3x=-1

x=-1/3

Is it the common method?

When you have to deal with mod, the methid metioned is the most convenient to use.