Find the Discriminant 3(x^2+16)=0

$3 (x^{2} + 16) = 0$

Step 1

Simplify the left side.

Simplify $3 (x^{2} + 16)$ .

Apply the distributive property.

$3 x^{2} + 3 \cdot 16 = 0$

Multiply $3$ by $16$ .

$3 x^{2} + 48 = 0$

Step 2

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

$b^{2} - 4 (a c)$

Step 3

Substitute in the values of $a$ , $b$ , and $c$ .

$0^{2} - 4 (3 \cdot 48)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

Raising $0$ to any positive power yields $0$ .

$0 - 4 (3 \cdot 48)$

Multiply $- 4 (3 \cdot 48)$ .

Multiply $3$ by $48$ .

$0 - 4 \cdot 144$

Multiply $- 4$ by $144$ .

$0 - 576$

Subtract $576$ from $0$ .

$- 576$