# How do you find the discriminant for 2.25x^2-3x=-1 and determine the number and type of solutions?

Apr 16, 2018

color(violet)(b^2 - 4ac = 0, " Given equation has one real repeated root " -(2/3)

#### Explanation:

$2.25 {x}^{2} - 3 x + 1 = 0$

$a = 2.25 , b = - 3 , c = 1$

$D = {b}^{2} - 4 a c = {\left(- 3\right)}^{2} - \left(4 \cdot 2.25 \cdot 1\right) = 9 - 9 = 0$

Since color(violet)(b^2 - 4ac = 0, " Given equation has one real repeated root "

$\text{and the root is } = \frac{b}{2 a} = - \frac{3}{2 \cdot 2.25} = - \frac{3}{4.5} = - \frac{2}{3}$