Question

which of the following is a solution to the quadratic equation 2x^2 - 5x = 6 assume that the solution has been rounded to the nearest hunderdth, if applicable

Answer 1

To find the solutions to the quadratic equation \(2x^2 - 5x = 6\), we first rewrite it in standard form:

\[
2x^2 - 5x - 6 = 0
\]

Next, we can use the quadratic formula:

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

where \(a = 2\), \(b = -5\), and \(c = -6\).

We'll first calculate the discriminant (\(b^2 - 4ac\)):

\[
b^2 - 4ac = (-5)^2 - 4(2)(-6)
\]
\[
= 25 + 48 = 73
\]

Now, substituting the values into the quadratic formula:

\[
x = \frac{-(-5) \pm \sqrt{73}}{2(2)}
\]
\[
= \frac{5 \pm \sqrt{73}}{4}
\]

Now we will calculate the two potential solutions:

1. \(x_1 = \frac{5 + \sqrt{73}}{4}\)
2. \(x_2 = \frac{5 - \sqrt{73}}{4}\)

We will approximate \(\sqrt{73}\):

\(\sqrt{73} \approx 8.544\)

Calculating \(x_1\):

\[
x_1 = \frac{5 + 8.544}{4} \approx \frac{13.544}{4} \approx 3.386
\]

Calculating \(x_2\):

\[
x_2 = \frac{5 - 8.544}{4} \approx \frac{-3.544}{4} \approx -0.886
\]

Thus, the solutions to the equation \(2x^2 - 5x - 6 = 0\) approximate to:

- \(x_1 \approx 3.39\) (rounded to the nearest hundredth)
- \(x_2 \approx -0.89\) (rounded to the nearest hundredth)

So, the solutions are approximately \(3.39\) and \(-0.89\).