Question

How to use the discriminant to find out what type of solutions the equation has for `x^2 - 3x + 4 = 0`?

Answer 1

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

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

For the given equation `x^2-3x+4 = 0`
`Delta = (-3)^2 -4(1)(4) <0`
So this equation has no Real solutions.

(It does however have 2 Complex solutions)