Find the Discriminant 3x^2+12x+5

$3 x^{2} + 12 x + 5$

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 $c$ .

$12^{2} - 4 (3 \cdot 5)$

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

Raise $12$ to the power of $2$ .

$144 - 4 (3 \cdot 5)$

Multiply $- 4 (3 \cdot 5)$ .

Multiply $3$ by $5$ .

$144 - 4 \cdot 15$

Multiply $- 4$ by $15$ .

$144 - 60$

Subtract $60$ from $144$ .

$84$