Polynomials Sprint: What I Learnt

In this note, you will write down 1 item that you learnt, from reading the chapter, working on the problem or understanding the note. State what you liked about it, and how it could be useful. You can also add additional things that you want to find out.

For example

I learnt about the rational root theorem, which says that the rational roots of a polynomial with integer coefficients depends only on the first and last coefficient. This gives us a simple way to test for possible roots of a polynomial. I would like to know if there is a "irrational root theorem", which tells us what other roots we could try, like \( \sqrt{2} \) or \( 1 + 2i \).

For more examples, see Adventures Of The Mind Diary.

Note by Calvin Lin
4 years, 4 months ago

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  Easy Math Editor

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2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

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I finally learned the real reason why f(x) has a root at x = a if and only if f(x) = (x-a)(g(x))--namely, from the remainder factor theorem. This makes problems like Polynomial Remainder trivial.

Colin Tang - 4 years, 4 months ago

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for a newcomer to Olympiad mathematics One word that describes Calvin sir......for his notes .....help......He is embodiment of wisdom who is sent to earth to help to nurture blooming minds to become torch bearers..for mathematics........

I have in my school learnt this theorem but the advance questions really was great ....I learnt how to apply this for hexamonic and heptamonic........so on polynomials

SIMPLY PUTTING SIR YOU ARE GREAT

Ashutosh Mahapatra - 4 years, 3 months ago

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Wait what

David Lee - 4 years, 3 months ago

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