To determine the value of the discriminant for the quadratic equation [tex]\(0 = 2x^2 + x - 3\)[/tex], we follow these steps:
1. Identify the coefficients [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] from the given quadratic equation. The equation is [tex]\(2x^2 + x - 3 = 0\)[/tex].
- Here, [tex]\(a = 2\)[/tex], [tex]\(b = 1\)[/tex], and [tex]\(c = -3\)[/tex].
2. Use the formula for the discriminant of a quadratic equation, which is given by:
[tex]\[
\Delta = b^2 - 4ac
\][/tex]
3. Substitute the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] into the discriminant formula:
[tex]\[
\Delta = (1)^2 - 4 \cdot 2 \cdot (-3)
\][/tex]
4. Perform the calculations step-by-step:
[tex]\[
\Delta = 1 - (4 \cdot 2 \cdot -3)
\][/tex]
[tex]\[
\Delta = 1 - (-24)
\][/tex]
[tex]\[
\Delta = 1 + 24
\][/tex]
[tex]\[
\Delta = 25
\][/tex]
Therefore, the value of the discriminant for the quadratic equation [tex]\(0 = 2x^2 + x - 3\)[/tex] is [tex]\( \boxed{25} \)[/tex].
