Find the Discriminant 2z^2+3z+2=0

$2 z^{2} + 3 z + 2 = 0$

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 $c$ .

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

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

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

$9 - 4 (2 \cdot 2)$

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

Multiply $2$ by $2$ .

$9 - 4 \cdot 4$

Multiply $- 4$ by $4$ .

$9 - 16$

Subtract $16$ from $9$ .

$- 7$