Question

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

Answer 1

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

Explanation:

`2.25x^2 - 3x + 1 = 0`

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

`D = b^2 - 4ac = (-3)^2 - (4 * 2.25 * 1) = 9 - 9 = 0`

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

`"and the root is " = b / (2a) = -3 / (2 * 2.25) = -3/4.5 = -2/3`