Description

• One homework problem that gave me significant difficulty was solving the quadratic equation using the quadratic formula: \( ax^2 + bx + c = 0 \). Specifically, the problem was \( 2x^2 – 4x – 6 = 0 \).At first, I had several misconceptions:1. I misunderstood the quadratic formula itself. I thought it was \( x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a} \), not realizing that the entire expression under the square root (\( b^2 – 4ac \)) is crucial and often miscalculated.2. I initially miscalculated the discriminant, leading to wrong solutions.Here’s how I approached solving it and the correct method I eventually learned:1. **Initial Incorrect Steps**: – I tried to plug in the values directly without properly simplifying the discriminant: \( b^2 – 4ac \).   – My incorrect calculation was: \( (-4)^2 – 4 \cdot 2 \cdot (-6) = 16 – 48 = -32 \), which is clearly incorrect because the discriminant should not be negative for this equation.2. **Correct Steps**: – First, correctly identify \( a = 2 \), \( b = -4 \), and \( c = -6 \).   – Calculate the discriminant properly: \[  b^2 – 4ac = (-4)^2 – 4 \cdot 2 \cdot (-6) = 16 + 48 = 64.     \]   – Apply the quadratic formula: \[  x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a} = \frac{-(-4) \pm \sqrt{64}}{2 \cdot 2} = \frac{4 \pm 8}{4}.     \]   – Simplify to get the two possible solutions: \[  x = \frac{4 + 8}{4} = 3 \quad \text{and} \quad x = \frac{4 – 8}{4} = -1.     \]**Resources and Learning**:- I consulted my textbook and re-watched lecture videos on solving quadratic equations.- I used NetTutor, which was helpful, but as with the example, it took a while to get a response. However, the feedback was clear and precise.- I also asked a friend who explained the importance of the discriminant and walked me through the proper application of the quadratic formula.From this experience, I learned the importance of correctly applying mathematical formulas and thoroughly understanding each component of the formula. Additionally, I realized the value of multiple resources for understanding challenging concepts. NetTutor and peer assistance were particularly beneficial in reinforcing the correct methods.

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