Dec 13, 2017

The discriminant is $- 28$, meaning there are no real solutions to the above function.

Explanation:

Given an equation in the form $a {x}^{2} + b x + c$ where $a \setminus \ne q 0$, the discriminant is given by ${b}^{2} - 4 a c$.

If . . .

${b}^{2} - 4 a c > 0 ,$ there are $2$ real solutions.

${b}^{2} - 4 a c = 0 ,$ there is $1$ real solution.

${b}^{2} - 4 a c < 0$, there are no real solutions.

In this case, the discriminant is ${10}^{2} - 4 \left(- 4\right) \left(- 8\right)$,

$\setminus \implies 100 - 128 \setminus \implies - 28$

$\setminus \therefore$ there are no real solutions.