Question

which of the following is a solution to the quadratic equation 2x^2 - 5x = 6

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 solve this equation using the quadratic formula:

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

In our equation, \(a = 2\), \(b = -5\), and \(c = -6\).

Now, we can calculate the discriminant:

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

Since the discriminant is positive, we have two real solutions. Now we can apply the quadratic formula:

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

Thus, the two solutions are:

\[
x = \frac{5 + \sqrt{73}}{4} \quad \text{and} \quad x = \frac{5 - \sqrt{73}}{4}
\]

If you have specific answer options, you can compare them to \( \frac{5 + \sqrt{73}}{4} \) and \( \frac{5 - \sqrt{73}}{4} \) to see if any match.