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Cubic computation (Posted on 2021-11-19) Difficulty: 3 of 5
Let a,b,c be real roots of the polynomial x3-px2+qx-r=0, where p,q,r∈R. Compute the product (a-b)(b-c)(c-a).

No Solution Yet Submitted by Danish Ahmed Khan    
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Some Thoughts Observation | Comment 1 of 3
First, depending on the order of the roots the product can be positive, negative, or zero.  If we consider them as a ≤ b ≤ c, the product will not be negative.

If r=0 the polynomial has a root at zero and two others can be found by the quadratic formula.  The product works out to q*sqrt(p^2-4q).

Edited on November 22, 2021, 10:56 am
  Posted by Jer on 2021-11-22 10:14:21

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