Question

Quadratic Formula is x=−b ± b2−4ac√2a


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

write in in quadratic formula form, and find the x= (lesser number), and x=(greater number).

Answer 1

The quadratic formula is given by:

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

For the equation \(3x^2 + 18x + 24 = 0\), we can identify the coefficients as follows:

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

Now, we can use these coefficients in the quadratic formula:

1. **Calculate \(b^2 - 4ac\):**

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

2. **Apply the values into the quadratic formula:**

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

3. **Calculate \(\sqrt{36}\):**

\[
\sqrt{36} = 6
\]

4. **Substitute this back into the formula:**

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

5. **Calculate the two possible values for \(x\):**

**First Value (lesser number):**

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

**Second Value (greater number):**

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

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

- \(x = -4\) (lesser number)
- \(x = -2\) (greater number)

Final answer:

- \(x = -4\) (lesser number)
- \(x = -2\) (greater number)