Question

How do you find the discriminant and how many solutions does `3x^2 - 5x + 4 = 0` have?

Answer 1

`3x^2-5x+4=0`

For a quadratic in the form
`ax^2+bx+c=0`
the discriminant is
`Delta = b^2-4ac`
where
`Delta {(<0 rarr "no solutions"),(=0 rarr 1 "solution"),(>0 rarr 2 "solutions"):}`

`Delta = b^2-4ac`

`= (-5)^2 -4(3)(4)`

`=25- 48 = -23`

`<0`

The given quadratic equation has no solutions.