What are some examples of quadratic equations?
An example of an AI chatbot conversation about quadratic equations and their applications.
What are some examples of quadratic equations?
Quadratic equations are in the form ax² + bx + c = 0. Examples include x² - 5x + 6 = 0 and 2x² + 3x - 2 = 0.
Can you explain how to solve one of these equations?
Sure! Let's solve x² - 5x + 6 = 0 using factoring. It factors to (x - 2)(x - 3) = 0, giving solutions x = 2 and x = 3.
What if the equation doesn't factor easily?
If it doesn't factor easily, you can use the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a.
Can you show me an example using the quadratic formula?
Of course! For 2x² + 3x - 2 = 0, a = 2, b = 3, c = -2. Plugging into the formula gives x = 0.5 and x = -2.
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