What kind of solutions does 4/3x^2 - 2x + 3/4 = 0  have?

Jun 27, 2015

$\frac{4}{3} {x}^{2} - 2 x + \frac{3}{4} = 0$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$has one Real solution

Explanation:

For a quadratic of the form $a {x}^{2} + b x + c = 0$
the discriminant $\Delta = {b}^{2} - 4 a c$ indicates the number and type of roots.

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

For $\frac{4}{3} {x}^{2} - 2 x + \frac{3}{4} = 0$

$\Delta = {\left(- 2\right)}^{2} - 4 \left(\frac{4}{3}\right) \left(\frac{3}{4}\right) = 0$