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

May 3, 2015

$3 {x}^{2} - 5 x + 4 = 0$

For a quadratic in the form
$a {x}^{2} + b x + c = 0$
the discriminant is
$\Delta = {b}^{2} - 4 a c$
where
$\Delta \left\{\begin{matrix}< 0 \rightarrow \text{no solutions" \\ =0 rarr 1 "solution" \\ >0 rarr 2 "solutions}\end{matrix}\right.$

$\Delta = {b}^{2} - 4 a c$

$= {\left(- 5\right)}^{2} - 4 \left(3\right) \left(4\right)$

$= 25 - 48 = - 23$

$< 0$

The given quadratic equation has no solutions.