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

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

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 $c$ .

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

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

Raise $4$ to the power of $2$ .

$16 - 4 (1 \cdot 5)$

Multiply $- 4 (1 \cdot 5)$ .

Multiply $5$ by $1$ .

$16 - 4 \cdot 5$

Multiply $- 4$ by $5$ .

$16 - 20$

Subtract $20$ from $16$ .

$- 4$