Find the Discriminant -5x^2-x-2=0

$- 5 x^{2} - x - 2 = 0$

Step 1

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

$b^{2} - 4 (a c)$

Step 2

Substitute in the values of $a$ , $b$ , and $c$ .

${(- 1)}^{2} - 4 (- 5 \cdot - 2)$

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

Raise $- 1$ to the power of $2$ .

$1 - 4 (- 5 \cdot - 2)$

Multiply $- 4 (- 5 \cdot - 2)$ .

Multiply $- 5$ by $- 2$ .

$1 - 4 \cdot 10$

Multiply $- 4$ by $10$ .

$1 - 40$

Subtract $40$ from $1$ .

$- 39$