# How do you use the discriminant to determine the nature of the solutions given  n^2 – 18n + 81 = 0?

Jan 19, 2017

The answer is $S = \left\{9\right\}$

#### Explanation:

We compare this equation to

$a {x}^{2} + b x + c = 0$

${n}^{2} - 18 n + 81 = 0$

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

$\Delta = {\left(- 18\right)}^{2} - 4 \cdot 1 \cdot 81 = 324 - 324 = 0$

As $\Delta = 0$, there is a double real root

$n = - \frac{b}{2 a} = \frac{18}{2} = 9$