Question

How to use the discriminant to find out what type of solutions the equation has for `2x^2 = 0`?

Answer 1

Your equation is in the form `ax^2+bx+c=0` where:
`a=2`
`b=0`
`c=0`
The discriminant is:
`Delta=b^2-4ac=0-0=0`
When `Delta=0` you will have two real coincident solutions.
In this case `x_1=x_2=0`

Answer 2

The discriminant for a parabolic equation of the form
`ax^2+bx+c = 0`
is
`Delta = b^2-4ac`

`Delta { (<0 rarr "no Real solutions"),(=0 rarr "1 Real solution"), (>0 rarr "2 Real solutions"):}`

`y=2x^2`
can be re-written in the form `y = ax^2+bx+c` as

`y = 2x^2 + (0)x + (0)`

and the discriminant becomes
`Delta = 0^2-4(2)(0) = 0`
which implies
there is 1 Real solution.