To determine which option correctly applies the quadratic formula to the given equation [tex]\(2x^2 - 9x + 4 = 0\)[/tex], let's first recall the quadratic formula:
[tex]\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\][/tex]
For our specific equation, [tex]\(a = 2\)[/tex], [tex]\(b = -9\)[/tex], and [tex]\(c = 4\)[/tex].
Let's substitute these values into the quadratic formula:
[tex]\[
x = \frac{-(-9) \pm \sqrt{(-9)^2 - 4 \cdot 2 \cdot 4}}{2 \cdot 2}
\][/tex]
Now let's compare this with the given options:
A. [tex]\(x = \frac{-9 \pm \sqrt{(-9)^2 - 4(2)(4)}}{2(2)}\)[/tex]
This option incorrectly uses [tex]\(-9\)[/tex] instead of [tex]\(-(-9)\)[/tex] which should be [tex]\(9\)[/tex]. Incorrect.
B. [tex]\(x = \frac{-(-9) = \sqrt{(-9) - 4(2)(4)}}{2(2)}\)[/tex]
This option incorrectly presents the formula, having an equals sign instead of a plus-minus symbol and an incorrect formula under the square root. Incorrect.
C. [tex]\(x = -(-9) \pm \sqrt{(-9)^2 - 4(2)(4)}\)[/tex]
This option does not divide by [tex]\(2a\)[/tex]. Incorrect.
D. [tex]\(x = \frac{-(-9) \pm \sqrt{(-9)^2 - 4(2)(4)}}{2(2)}\)[/tex]
This option correctly substitutes the values into the quadratic formula.
Thus, option D is the correct application of the quadratic formula to the given equation.
