Find the Discriminant 4x^2+7x+5=0

$4 x^{2} + 7 x + 5 = 0$

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 $c$ .

$7^{2} - 4 (4 \cdot 5)$

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

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

$49 - 4 (4 \cdot 5)$

Multiply $- 4 (4 \cdot 5)$ .

Multiply $4$ by $5$ .

$49 - 4 \cdot 20$

Multiply $- 4$ by $20$ .

$49 - 80$

Subtract $80$ from $49$ .

$- 31$