To identify the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] in the quadratic equation [tex]\(0 = \frac{1}{2}x^2 - 3x - 2\)[/tex], we need to compare this equation to the general form of a quadratic equation:
[tex]\[ ax^2 + bx + c = 0 \][/tex]
By comparing term by term with [tex]\( 0 = \frac{1}{2}x^2 - 3x - 2 \)[/tex], we observe:
- The coefficient of [tex]\(x^2\)[/tex] is [tex]\(\frac{1}{2}\)[/tex]. Therefore, [tex]\(a = \frac{1}{2}\)[/tex].
- The coefficient of [tex]\(x\)[/tex] is [tex]\(-3\)[/tex]. Therefore, [tex]\(b = -3\)[/tex].
- The constant term is [tex]\(-2\)[/tex]. Therefore, [tex]\(c = -2\)[/tex].
Thus, the values are:
[tex]\[ a = \frac{1}{2}, \ b = -3, \ c = -2 \][/tex]
So, the correct choice is:
[tex]\[ \boxed{a = \frac{1}{2}, b = -3, c = -2} \][/tex]
