Find the Discriminant 2h^2+7h+4=0

$2 h^{2} + 7 h + 4 = 0$

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 $c$ .

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

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

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

$49 - 4 (2 \cdot 4)$

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

Multiply $2$ by $4$ .

$49 - 4 \cdot 8$

Multiply $- 4$ by $8$ .

$49 - 32$

Subtract $32$ from $49$ .

$17$