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

[Jhenrique]

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.

 

[AlephZero]

It is not possible. A polynomial x³+bx²+cx+d can have three different real roots. A polynomial At³+B can not.