Question

Using the quadratic formula, find the solution to 3x2+18x+24=0 (1 point) Responses x=4 x is equal to 4 x=−2 x is equal to negative 2 x=4, x=2 x=4, x=2 x=−2, x=−4

Answer 1

To solve the quadratic equation \(3x^2 + 18x + 24 = 0\) using the quadratic formula, we start by identifying the coefficients:

- \(a = 3\)
- \(b = 18\)
- \(c = 24\)

The quadratic formula is given by:

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

Now, we need to calculate the discriminant \(b^2 - 4ac\):

\[
b^2 = 18^2 = 324
\]
\[
4ac = 4 \cdot 3 \cdot 24 = 288
\]
\[
b^2 - 4ac = 324 - 288 = 36
\]

Now, we can plug the values into the quadratic formula:

\[
x = \frac{-18 \pm \sqrt{36}}{2 \cdot 3}
\]

Calculating the square root of the discriminant:

\[
\sqrt{36} = 6
\]

Now substituting this back into the formula:

\[
x = \frac{-18 \pm 6}{6}
\]

This gives us two potential solutions:

1. When we use the positive root:

\[
x = \frac{-18 + 6}{6} = \frac{-12}{6} = -2
\]

2. When we use the negative root:

\[
x = \frac{-18 - 6}{6} = \frac{-24}{6} = -4
\]

Thus, the solutions to the equation \(3x^2 + 18x + 24 = 0\) are:

\[
x = -2 \quad \text{and} \quad x = -4
\]

Therefore, the correct answer from the choices given is:

**x = −2, x = −4**.