A triangle has sides of lengths 7, 24, and 25. Verify if it is a right triangle using the Pythagorean theorem.
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- Solve \(n^2 + n - 420 = 0\) using the quadratic formula:
- \(n = \frac{-1 \pm \sqrt{1 + 1680}}{2} = \frac{-1 \pm 41}{2}\).
- The positive solution is \(n = 20\).
- Check \(7^2 + 24^2 = 25^2\).
- Calculate: \(49 + 576 = 625\).
- #### Yes, it is a right triangle.Question: A medical AI researcher models diagnostic accuracy using a polynomial $ p(x) $ such that $ p(1) = 3 $, $ p(2) = 10 $, $ p(3) = 21 $, and $ p(4) = 36 $. If $ p(x) $ is a cubic polynomial, find $ p(0) $.
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