Find the Discriminant x^2-3x-7=0

$x^{2} - 3 x - 7 = 0$

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 $c$ .

${(- 3)}^{2} - 4 (1 \cdot - 7)$

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

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

$9 - 4 (1 \cdot - 7)$

Multiply $- 4 (1 \cdot - 7)$ .

Multiply $- 7$ by $1$ .

$9 - 4 \cdot - 7$

Multiply $- 4$ by $- 7$ .

$9 + 28$

Add $9$ and $28$ .

$37$