Find the Discriminant 2p^2+5p-4=0

$2 p^{2} + 5 p - 4 = 0$

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 $c$ .

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

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

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

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

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

Multiply $2$ by $- 4$ .

$25 - 4 \cdot - 8$

Multiply $- 4$ by $- 8$ .

$25 + 32$

Add $25$ and $32$ .

$57$