Find the Discriminant x^2-7x-4=0

$x^{2} - 7 x - 4 = 0$

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 $c$ .

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

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

Raise $- 7$ to the power of $2$ .

$49 - 4 (1 \cdot - 4)$

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

Multiply $- 4$ by $1$ .

$49 - 4 \cdot - 4$

Multiply $- 4$ by $- 4$ .

$49 + 16$

Add $49$ and $16$ .

$65$