Compute the discriminant, $$ d=b^{2}-4 a c $$, of the quadratic equation $$ 2 x^{2}+3 x+4=0 $$ $$ d=4 $$ $$ d=9 $$ $$ d=-23 $$ $$ d=72 $$

Question

UpStudy AI · Accepted Answer

To compute the discriminant $$ d $$ of the quadratic equation $$ 2x^{2} + 3x + 4 = 0 $$, we'll use the formula:

$$
d = b^{2} - 4ac
$$

Here, the coefficients are:
- $$ a = 2 $$
- $$ b = 3 $$
- $$ c = 4 $$

Substituting these values into the formula:

$$
d = 3^{2} - 4 \times 2 \times 4 = 9 - 32 = -23
$$

**Therefore, the discriminant is $$ d = -23 $$.**

Among the provided options:
- $$ d = 4 $$
- $$ d = 9 $$
- $$ d = -23 $$
- $$ d = 72 $$

The correct answer is:

**$$ d = -23 $$**
The discriminant $$ d $$ is $$ -23 $$.

Compute the discriminant, \( d=b^{2}-4 a c \), of the quadratic equation \( 2 x^{2}+3 x+4=0 \) \( d=4 \) \( d=9 \) \( d=-23 \) \( d=72 \)