MAT - Paper 2012 - Q3
Flashcards
The normal equation of a cubic is
\[ax^3 + bx^2 + cx + d\]When trying to find a cubic (or really any function) with certain properties, why shouldn’t you stick to using this?? Because you can often use the properties the answer must have to come up with a much more concise representation.
Instead of
\[x^3 + ax^2 + bx + c\]what could you use to represent a cubic you know has to have a repeated root at $x = 0$??
\[x^2(x - t)\]If the distance between the two stationary points of a cubic is $d$, and you’ve constructed a new cubic with the stationary point at the origin, where must the next stationary point be?
\[0 + d = d\]