Can a Polynomial be Transformed to Eliminate its Quadratic and Linear Terms?

  • Thread starter Thread starter Jhenrique
  • Start date Start date
  • Tags Tags
    Polynomials
AI Thread Summary
Transforming a polynomial of the form p(x) = ax³ + bx² + cx + d into a form like p(t) = At³ + B while eliminating both quadratic and linear terms is not feasible. The discussion highlights that a cubic polynomial can have three distinct real roots, whereas a polynomial of the form At³ + B cannot accommodate this characteristic. Attempts to achieve such a transformation have not been successful. The conclusion drawn is that it is impossible to eliminate both the quadratic and linear terms in this context. Therefore, the transformation sought cannot be accomplished.
Jhenrique
Messages
676
Reaction score
4

Homework Statement


I want to transform a polynomial of kind p(x)=ax³+bx²+cx+d in another like p(t)=At³+B. Is possible?

Homework Equations


Is possible to transform a polynomial of kind ax³+bx²+cx+d in another like t³+pt+q.
https://en.wikipedia.org/wiki/Cubic_formula#Reduction_to_a_depressed_cubic
But, I wish to eliminate the quadratic term and the linear term too.

The Attempt at a Solution


None well successful that compensates write here.
 
Physics news on Phys.org
It is not possible. A polynomial x³+bx²+cx+d can have three different real roots. A polynomial At³+B can not.
 

Similar threads

I Quintic Polynomial Tschirnhaus Transform: Possible complex Bring Radicals
Replies
0
Views
2K
I Want to understand how to express the derivative as a matrix
Replies
8
Views
2K
MHB Evaluate the constant in polynomial function
Replies
7
Views
1K
Prove: polynomial is uniquely defined by three of its values
Replies
2
Views
2K
Linear Transformations p2 to R2
Replies
16
Views
4K
Finding the basis for a set of polynomials (linear algebra)
Replies
1
Views
6K
Linear Algebra - Linearity of a transformation
Replies
4
Views
1K
Solving Linear System of Equations: Elimination
Replies
2
Views
4K
I Canonical Form for quadratic equations *with* linear terms
Replies
4
Views
3K
Quadratic Equations: Homework on Non-Real Roots
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top