Question

Use the quadratic formula to answer the questions below.

Quadratic Formula is x=−b ± b2−4ac√2a


The equation is 3x2+18x+24=0


Fill in the blanks below (yellow boxes).

(1 point)

Answer 1

To use the quadratic formula, we need to identify the values of \( a \), \( b \), and \( c \) from the quadratic equation \( 3x^2 + 18x + 24 = 0 \).

From the equation:
- \( a = 3 \)
- \( b = 18 \)
- \( c = 24 \)

Now, we will use the quadratic formula:

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

Now, let's fill in the necessary values:

1. Calculate \( b^2 \):
\[
b^2 = 18^2 = 324
\]

2. Calculate \( 4ac \):
\[
4ac = 4 \cdot 3 \cdot 24 = 288
\]

3. Calculate the discriminant, \( b^2 - 4ac \):
\[
b^2 - 4ac = 324 - 288 = 36
\]

4. Now substitute these values into the quadratic formula:
\[
x = \frac{-18 \pm \sqrt{36}}{2 \cdot 3}
\]

5. Calculate \( \sqrt{36} \):
\[
\sqrt{36} = 6
\]

6. Substitute back into the quadratic formula:
\[
x = \frac{-18 \pm 6}{6}
\]

Now we can solve for the two potential values of \( x \):

1. First solution:
\[
x = \frac{-18 + 6}{6} = \frac{-12}{6} = -2
\]

2. Second solution:
\[
x = \frac{-18 - 6}{6} = \frac{-24}{6} = -4
\]

Thus, the solutions to the equation \( 3x^2 + 18x + 24 = 0 \) are \( x = -2 \) and \( x = -4 \).

If you were looking for specific answers to fill in the yellow boxes, they would be:

- \( a \) = 3
- \( b \) = 18
- \( c \) = 24
- \( b^2 = 324 \)
- \( 4ac = 288 \)
- \( b^2 - 4ac = 36 \)
- \( \sqrt{b^2 - 4ac} = 6 \)
- Solutions: \( x = -2 \) and \( x = -4 \)