Find the Discriminant x^2+2x+3=0

$x^{2} + 2 x + 3 = 0$

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 $c$ .

$2^{2} - 4 (1 \cdot 3)$

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

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

$4 - 4 (1 \cdot 3)$

Multiply $- 4 (1 \cdot 3)$ .

Multiply $3$ by $1$ .

$4 - 4 \cdot 3$

Multiply $- 4$ by $3$ .

$4 - 12$

Subtract $12$ from $4$ .

$- 8$