Find the Discriminant 2x^2+4X+3=0

$2 x^{2} + 4 X + 3 = 0$

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

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

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

$0^{2} - 4 (2 (4 X + 3))$

Evaluate the result to find the discriminant.

Simplify each term.

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

$0 - 4 (2 (4 X + 3))$

Apply the distributive property.

$0 - 4 (2 (4 X) + 2 \cdot 3)$

Multiply $4$ by $2$ .

$0 - 4 (8 X + 2 \cdot 3)$

Multiply $2$ by $3$ .

$0 - 4 (8 X + 6)$

Apply the distributive property.

$0 - 4 (8 X) - 4 \cdot 6$

Multiply $8$ by $- 4$ .

$0 - 32 X - 4 \cdot 6$

Multiply $- 4$ by $6$ .

$0 - 32 X - 24$

Subtract $32 X$ from $0$ .

$- 32 X - 24$