Question

Which of the following is a solution to the quadratic equation 2x2−5x=6 ? Assume that the solution has been rounded to the nearest hundredth, if applicable.(1 point)Responsesx=1.03x equals 1.03x=0.89x equals 0.89x=−0.89x equals negative 0.89x=−1.03

Answer 1

To solve the equation \(2x^2 - 5x = 6\), we first rearrange it into standard quadratic form. We do this by subtracting 6 from both sides:

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

Next, we can use the quadratic formula to find the roots of the equation. The quadratic formula is given by:

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

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

We start by calculating the discriminant (\(b^2 - 4ac\)):

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

Now we can apply the formula:

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

Calculating \(\sqrt{73}\) gives approximately \(8.54\). Now, substitute this value back into the formula:

1. For the positive root:
\[
x = \frac{5 + 8.54}{4} = \frac{13.54}{4} \approx 3.385
\]

2. For the negative root:
\[
x = \frac{5 - 8.54}{4} = \frac{-3.54}{4} \approx -0.885
\]

Rounding to the nearest hundredth, we have:

- The positive solution is \(x \approx 3.39\).
- The negative solution is \(x \approx -0.89\).

Among the options provided, the correct solution rounded to the nearest hundredth is:

**\(x = -0.89\)**.