Find the Discriminant -4x^2-5x-2=0

$- 4 x^{2} - 5 x - 2 = 0$

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 $c$ .

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

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

Raise $- 5$ to the power of $2$ .

$25 - 4 (- 4 \cdot - 2)$

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

Multiply $- 4$ by $- 2$ .

$25 - 4 \cdot 8$

Multiply $- 4$ by $8$ .

$25 - 32$

Subtract $32$ from $25$ .

$- 7$