Question

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

Answer 1

`2x^2-3x+4` is of the form `ax^2+bx+c`, with `a=2`, `b=-3` and `c=4`.

The discriminant can be calculated using the formula as follows:

`Delta = b^2-4ac = (-3)^2-(4xx2xx4) = 9-32 = -23`

This is negative, so `2x^2-3x+4 = 0` has two distinct complex roots and no real roots.

The possible cases are:

`Delta > 0` : Two distinct real roots.
`Delta = 0` : One repeated real root.
`Delta < 0` : No real roots (two distinct complex ones).