#Quadratics

22 messages · Page 1 of 1 (latest)

tulip surge
buoyant rockBOT
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tulip surge
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How to proceed

glad oriole
tulip surge
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b² - 4ac <= 0

glad oriole
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Ohh I misread the question the roots can be complex as well then

tulip surge
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It's fine ig. I feel like minimum value would be related to =0 case. Just being cautious and added <

tulip surge
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What do I do next

whole gale
# tulip surge What do I do next

You need to find the minimum value of z = 5a + b under the constraint b^2 - 20a ≤ 0.
How can we usually find extrema of a function under a constraint?

unique crane
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Linear Programming?

tulip surge
whole gale
# tulip surge Hmmm restrict a,b using the constraint then find the minimum of x for those a,b?

There isn't an x here. The general algorithm is as follows.
Suppose you have a function f and some constraints that form a region D.

  1. Find the critical points of f that lie in the interior of D. If D is unbounded, check which ones are extremum points.
  2. Do the same, but for the boundary of D (you may need to parametrize the boundary or use Lagrange multipliers or bordered hessian; if the boudary is sufficiently simple, you can just reduce the amount of variables).
  3. Compare the values at all the extremum points you've found.
tulip surge
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Hmmmm looks tedious

tulip surge
crimson reef
tulip surge
# crimson reef

Oh yeah thank you I made a mistake after finding |b| inequality so didn't get to a reasonable answer

sullen radishBOT
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@tulip surge has given 1 rep to @crimson reef

tulip surge
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+close