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

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

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 $c$ .

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

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

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

$25 - 4 (1 \cdot 2)$

Multiply $- 4 (1 \cdot 2)$ .

Multiply $2$ by $1$ .

$25 - 4 \cdot 2$

Multiply $- 4$ by $2$ .

$25 - 8$

Subtract $8$ from $25$ .

$17$