Question

Quadratic Formula is x=−b ± b2−4ac√2a


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

write in in wquadratic formula form.

Answer 1

To express the quadratic equation \(3x^2 + 18x + 24 = 0\) in terms of the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), we need to identify the coefficients \(a\), \(b\), and \(c\).

From the equation \(3x^2 + 18x + 24 = 0\):

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

Now, we'll substitute these values into the quadratic formula:

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

Substituting the values of \(a\), \(b\), and \(c\):

\[
x = \frac{-18 \pm \sqrt{18^2 - 4 \cdot 3 \cdot 24}}{2 \cdot 3}
\]

Calculating \(b^2 - 4ac\):

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

Now substituting back into the formula:

\[
x = \frac{-18 \pm \sqrt{36}}{6}
\]

Calculating the square root:

\[
\sqrt{36} = 6
\]

Now we can write the final expression:

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

This simplifies to two solutions:

1. \(x = \frac{-18 + 6}{6} = \frac{-12}{6} = -2\)
2. \(x = \frac{-18 - 6}{6} = \frac{-24}{6} = -4\)

Thus, the quadratic formula form for the equation \(3x^2 + 18x + 24 = 0\) is:

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