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

May 22, 2015

Given a parabolic equation in the form
$a {x}^{2} + b x + c = 0$
the discriminant is
$\Delta = {b}^{2} - 4 a c$

$\Delta \left\{\begin{matrix}< 0 \rightarrow \text{ no Real solutions" \\ =0 rarr "1 Real solution" \\ >0 rarr "2 Real solutions}\end{matrix}\right.$

For the given equation ${x}^{2} - 3 x + 4 = 0$
$\Delta = {\left(- 3\right)}^{2} - 4 \left(1\right) \left(4\right) < 0$
So this equation has no Real solutions.

(It does however have 2 Complex solutions)