Question 1209700
<pre>

{{{f(x) = x^4 - 5x^3 + 5x^2 + 17x - 42 + 4x^4 + 10x^3 - 18x^2 + 2x - 5}}}

I smell a rat!!! And not just because of the approximate AI solution, allegedly
posted by CPhill(682).

Finding roots of quartics (4th degree polynomial equations) such as this one,
which is solvable only by using Ferrari's method, is a very advanced algebraic
topic which would only be taught in an advanced university course.  I studied
both Cardano's method for solving the general cubic, and Ferrari's method for
solving the general quartic as a university junior, in a course which, back
then, was called "Theory of Equations".  

So why would a teacher assigning such an advanced problem as this, give the
quartic in the form above, instead of giving it in the form where all the like
terms were already combined, namely, like this:

{{{f(x)=5x^4 + 5x^3 - 13x^2 + 19x - 47}}}

This is not a quartic polynomial with rational roots that can be solved by
the P/Q method and synthetic division.  It can only be solved in terms of
radicals using Ferrari's method. 
  
Teachers of such advanced topics as this DO NOT assign problems in forms that
test them to see if they understand one of the most elementary topics of
beginning algebra, taught in middle school, i.e., that of 'combining like terms'.

This is like a chemistry professor testing chemistry students taking advanced
university chemistry courses, such as qualitative or quantitative analysis, if
they know that the chemical formula for water is H<sub>2</sub>O.   

Thus, I strongly suspect this problem is bogus, posted by a troll.

Edwin</pre>