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Home » x^2 - x - 6 = 0 - Midis

x^2 - x - 6 = 0 - Midis

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 In the fourth: $ x + y \leq 0, x - y \geq 0 \Rightarrow -2y $

📌 $ 2|x| \leq 8 \Rightarrow |x| \leq 4 $

📌 $ 2|y| \leq 8 \Rightarrow |y| \leq 4 $

📌 Thus, the region is a square with side length 4, bounded by $ |x| \leq 4 $, $ |y| \leq 4 $, and symmetric across both axes.

📌 This is a square centered at the origin with vertices at $ (\pm4, 0), (0, \pm4) $. The area is:

📌 \text{Area} = \frac{1}{2} \cdot \text{diagonal}_1 \cdot \text{diagonal}_2 = \frac{1}{2} \cdot 8 \cdot 8 = 32

📌 Question: A robotics engineer is calibrating a sensor whose response curve follows the cubic polynomial $ f(x) $ such that $ f(1) = 3, f(2) = -1, f(3) = 5, f(4) = 11 $. Find $ f(0) $.

📌 Solution: Let $ f(x) = ax^3 + bx^2 + cx + d $. Use the given values to form a system of equations:

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