Question

How to use the discriminant to find out what type of solutions the equation has for `4x^2 + 1 = 0`?

Answer 1

Written in the standard form for a quadratic `ax^2+bx+c=0`

`4x^2 + 1 = 0`
becomes
`4x^2 +(0)x +1 = 0`

The discriminant `Delta = b^2 - 4ac`
becomes
`Delta = -16`

`Delta { (<0 rarr "no Real roots (onlt Complex roots)"), (=0 rarr "1 Real root"),(>0 rarr "2 Real roots"):}`

Therefore
`4x^2+1 = 0` has only Complex roots