Sunday, 22 December 2019

Fun With Numbers

We were always taught that there are three ways to solve a quadratic equation i.e. something in the format Ax^2 + Bx +C = 0 - factorisation, the quadratic formula and completing the square  (see Cliff Notes).

Maths genius Po-Shen Loh has finally realised (or finally admitted?) that at this is all Emperor's New Clothes stuff (which maths people have used to show off and/or torture generations of pupils), and has explained a method that is so blindingly simple and obvious that a load of people - including me - are thinking "Damn! Why didn't I think of that?" (ignore the ghastly soundtrack):

The beauty of it is, even if you forget the precise steps, as long as you understand the logic in his video (which I won't bother paraphrasing, just watch the video starting at 1 min 46 seconds, it takes him less than a minute to explain), you can reverse engineer this method yourself.

1. Make sure that A = 1, so if you are given 2x^2 - 16x + 30 = 0, divide it all by 2 to get x^2 - 8x + 15 = 0.

2. Divide B by 2 and square it; deduct C (NB, if the constant at the end is negative, then add it!); then find the square root of the result, that is our new number "u" (I don't know why he chose "u").

3. x is then negative half of B, plus or minus "u".

For example:

x^2 - 8x + 15 = 0

16 - 15 = 1, the square root of 1 = +/- 1 ("u" in his notation).

x = 4 +/- 1 = 3 or 5.

Apparently it works in all circumstances, even if the answers are fractions or include the square root of a negative number.


Rational Anarchist said...

This is just a rearrangement of the quadratic formula, with a=1.

Mark Wadsworth said...

RA, sure, but it is simple and obvious, requires no memorising.

Derek said...

Cool. Thanks for spreading the word!