Find the Discriminant x^2+3x+1=0

$x^{2} + 3 x + 1 = 0$

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 $c$ .

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

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

Raise $3$ to the power of $2$ .

$9 - 4 (1 \cdot 1)$

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

Multiply $1$ by $1$ .

$9 - 4 \cdot 1$

Multiply $- 4$ by $1$ .

$9 - 4$

Subtract $4$ from $9$ .

$5$