# How do you find the discriminant and how many solutions does 1= -9x + 11x^2 have?

May 5, 2015

For a quadratic equation in standard form: $a {x}^{2} + b x + c = 0$
the discriminant is $\Delta = {b}^{2} - 4 a c$

First rearrange the given equation into standard form
$1 = - 9 x + 11 {x}^{2}$

11x^2-9x -1 =0#

Evaluate the discriminant:
$\Delta = {\left(- 9\right)}^{2} - 4 \left(11\right) \left(- 1\right)$
$= 81 + 44 = 125$

Since the solutions to a quadratic can be evaluated by the formula
$x = \frac{- b \pm \sqrt{\Delta}}{2 a}$
It follows that
$\Delta \left\{\begin{matrix}< 0 \rightarrow \text{no Real solutions" \\ =0rarr "1 Real solution" \\ >0rarr "2 Real solutions}\end{matrix}\right.$

For this example, $\Delta > 0$
therefore there are 2 Real solutions