Find the Discriminant 3z^2+6z+3=0

$3 z^{2} + 6 z + 3 = 0$

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 $c$ .

$6^{2} - 4 (3 \cdot 3)$

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

Raise $6$ to the power of $2$ .

$36 - 4 (3 \cdot 3)$

Multiply $- 4 (3 \cdot 3)$ .

Multiply $3$ by $3$ .

$36 - 4 \cdot 9$

Multiply $- 4$ by $9$ .

$36 - 36$

Subtract $36$ from $36$ .

$0$