Question

How do you find the discriminant and how many solutions does `y= x^2 + 3x` have?

Answer 1

The discriminant of an expression `ax^2+bx+c` is
`Delta = b^2-4ac`
(extracted from the quadratic formula for solutions
`x= (-b+-sqrt(Delta))/(2a)`

Extend the quadratic in the given equation so it looks like the general form:
`y = (1)x^2 +3x +0`

`Delta = 3^2-4(1)(0) = 9`

If you look back to the quadratic formula you can see:

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

In our case `Delta>0`
so `y=x^2+3x` has 2 solutions