# MAT - Paper 2012 - Q3

> Source: https://ollybritton.com/notes/maths/problems/mat/2012/q3/ · Updated: 2021-08-15 · Tags: mat, maths, notes

## 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??
$$
0 + d = d
$$

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