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Which shows the correct substitution of the values [tex]\(a, b\)[/tex], and [tex]\(c\)[/tex] from the equation [tex]\(0 = -3x^2 - 2x + 6\)[/tex] into the quadratic formula?

Quadratic formula: [tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]

A. [tex]\[ x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(-3)(0)}}{2(-3)} \][/tex]

B. [tex]\[ x = \frac{-2 \pm \sqrt{2^2 - 4(-38)}}{2(-3)} \][/tex]

C. [tex]\[ x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(3)(6)}}{2(3)} \][/tex]

D. [tex]\[ x = \frac{-2 \pm \sqrt{2^7 - 40}}{209} \][/tex]



Answer :

GinnyAnswer
Let's begin with the given quadratic equation:

[tex]\[ 0 = -3x^2 - 2x + 6 \][/tex]

We need to substitute the values [tex]\( a = -3 \)[/tex], [tex]\( b = -2 \)[/tex], and [tex]\( c = 6 \)[/tex] into the quadratic formula:

[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]

Let's break down each component of the quadratic formula step-by-step:

1. Substitute [tex]\( b \)[/tex]:

[tex]\[ -(-2) = 2 \][/tex]

2. Calculate [tex]\( b^2 \)[/tex]:

[tex]\[ (-2)^2 = 4 \][/tex]

3. Calculate [tex]\( 4ac \)[/tex]:

[tex]\[ 4 \cdot (-3) \cdot 6 = 4 \cdot -18 = -72 \][/tex]

4. Calculate the discriminant ([tex]\( b^2 - 4ac \)[/tex]):

[tex]\[ 4 - (-72) = 4 + 72 = 76 \][/tex]

5. Calculate [tex]\( 2a \)[/tex]:

[tex]\[ 2 \cdot (-3) = -6 \][/tex]

Thus, the correct values substituted into the quadratic formula from the given equation, taking [tex]\( a = -3 \)[/tex], [tex]\( b = -2 \)[/tex], and [tex]\( c = 6 \)[/tex], are:

[tex]\[ x = \frac{2 \pm \sqrt{76}}{-6} \][/tex]

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