To find the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] in the quadratic equation [tex]\(0 = 5x - 4x^2 - 2\)[/tex], let's examine the standard form of a quadratic equation. The standard form of a quadratic equation is given by:
[tex]\[ ax^2 + bx + c = 0 \][/tex]
We need to match the given equation [tex]\(0 = 5x - 4x^2 - 2\)[/tex] to the standard form. To do this, we'll reorganize the terms to align it explicitly with [tex]\( ax^2 + bx + c = 0 \)[/tex]:
[tex]\[ -4x^2 + 5x - 2 = 0 \][/tex]
Now, we can clearly identify the coefficients as follows:
- [tex]\(a\)[/tex] is the coefficient of [tex]\(x^2\)[/tex],
- [tex]\(b\)[/tex] is the coefficient of [tex]\(x\)[/tex],
- [tex]\(c\)[/tex] is the constant term.
From the equation [tex]\(-4x^2 + 5x - 2 = 0\)[/tex]:
- The coefficient of [tex]\(x^2\)[/tex] is [tex]\(-4\)[/tex], so [tex]\(a = -4\)[/tex].
- The coefficient of [tex]\(x\)[/tex] is [tex]\(5\)[/tex], so [tex]\(b = 5\)[/tex].
- The constant term is [tex]\(-2\)[/tex], so [tex]\(c = -2\)[/tex].
Therefore, the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] are:
[tex]\[ a = -4, \; b = 5, \; c = -2 \][/tex]
So, the correct answer is:
[tex]\[ a = -4, \; b = 5, \; c = -2 \][/tex]
Hence, the correct option is:
[tex]\[ \boxed{a = -4, b = 5, c = -2} \][/tex]
