Answer by Daniel Lichtblau for Solving a polynomial equation with a condition...
Could doSolve[{x^3 - p x^2 + q x - r == 0, r1 + r2 + r3 == p, r1 == r2, r1*r2 + r1*r3 + r2*r3 == q, r1*r2*r3 == r}, {r1, r2, r3}, {x, p}]The requirement of a double root places a relation on {p,q,r},...
View ArticleAnswer by bill s for Solving a polynomial equation with a condition of...
Equating coefficients makes sense: the polynomial x^3 - p x^2 + q x - r must be equal to Expand[(x - a)^2 (x - b)]-a^2 b + a^2 x + 2 a b x - 2 a x^2 - b x^2 + x^3Hencep == b + 2 aq == a^2 + 2 a br ==...
View ArticleAnswer by Szabolcs for Solving a polynomial equation with a condition of...
I would approach the problem like this:f[x_] := x^3 - p x^2 + q x - rNow try Solve[{f[x]==0, f'[x]==0}, x]which returns {} meaning that there are no solutions. More specifically it means that there are...
View ArticleAnswer by b.gates.you.know.what for Solving a polynomial equation with a...
I would say that if your polynomial has two identical roots then :$$x^3 - p x^2 + q x - r == (x - xs)^2 (x - xd)$$and you can solve for the unknowns xs, xs in terms of the other parameters.sol =...
View ArticleSolving a polynomial equation with a condition of equality on roots
Let the following equation have two equal roots:f[x_] := x^3 - p x^2 + q x - r And I want to find out what the three roots are. Not knowing how to put this condition within a Solve or Reduce, I have to...
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