Discriminant: \(b^2 - 4ac = (-4)^2 - 4 \times 2 \times (-6) = 16 + 48 = 64\)
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- Solve the quadratic equation \(2x^2 - 4x - 6 = 0\) using the quadratic formula.
- Quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
- Here, \(a = 2\), \(b = -4\), \(c = -6\)
- \(x = \frac{4 \pm \sqrt{64}}{4} = \frac{4 \pm 8}{4}\)
- Solutions: \(x = \frac{12}{4} = 3\) and \(x = \frac{-4}{4} = -1\)
- A train travels 180 miles in 3 hours. What is the average speed of the train in miles per hour?
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