Ask Uncle Colin: A Complex Roots Problem | Colin

Dear Uncle Colin,

I had a question in an exam that gave a cubic, $f(x) = x^3 – 8x^2 + cx + d$, with roots $\alpha$, $\beta$ and $\gamma$. When plotted on an Argand diagram, the triangle formed by the three roots has area 8. Given that $\alpha=2$, find $c$ and $d$. I couldn’t get near it – any ideas?

– Failed At Complex Task, Only Real Solution

Hi, FACTORS, and thanks for your message!

There are several steps to getting to the bottom of this, but the key one is that the roots of the polynomial $ax^n + bx^{n-1} + …=0$ sum to $-\frac{b}{a}$. You’ll definitely have seen that with…

Continue reading at:
https://ift.tt/2wNAeZy

Advertisements

Wrong, But Useful: Episode 56 | Colin

In Episode 56 of Wrong, But Useful, we’re joined by @zoelgriffiths (Zoe Griffiths), maths communicator from Think Maths.
Zoe had her poem e, to thee, x in @chalkdustmagazine recently, and did a set about misleading statistics at @aeoud (An Evening Of Unnecessary Detail)
Bad polls and fake stats, including this from the Mirror and a report on breast cancer screening, righteously rubbished by @dspiegel
Number of the podcast: 477277, a prime that would probably get you a taxi (and, indeed, would – if you were in Bolsover – thanks, @mathsjamPOR.)
Colin has upgraded his experience of G4G from…

Continue reading at:
https://ift.tt/2L3UKrY

Me, Jack and Hugh (Yin and Yang?) | charliecountryboy

And you thought there was just ‘lil, ol’ me.’ It’s funny but I only became aware of these guys about 20 years ago. You see, Hugh is the nice guy, (sunny side) he was a nice kid and when we were growing up on the farm he had total control.

Then, when I was 10 years-old we moved to Bradford and having  had the s*** kicked out of us for the first three months someone else had to take control, enter Jack (shady side). He’s not evil, but he didn’t believe in forever or that everyone has a good side or that disputes can be settled calmly and without confrontation. In fact he would…

Continue reading at:
https://ift.tt/2rGse6N

Review: Genius at Play, by Siobhan Roberts | Colin

It turns out, I made an error in Cracking Mathematics. Not (in this case) a mathematical or historical error, although there are plenty of those1 but an error of etiquette: my potted biography of John Horton Conway emphasised the Game of Life above the rest of his work; I imagine the book made a satisfying thud as he threw it aside.

Siobhan Roberts’s biography of Conway, Genius at Play (about £13 at the time of writing), goes into rather more detail about Conway’s achievements: the ATLAS of groups, monstrous moonshine and surreal numbers, to pick a few off the top of my head – and his…

Continue reading at:
https://ift.tt/2IgRATS

Me, Jack and Hugh (Yin and Yang?) | charliecountryboy

And you thought there was just ‘lil, ol’ me.’ It’s funny but I only became aware of these guys about 20 years ago. You see, Hugh is the nice guy, (sunny side) he was a nice kid and when we were growing up on the farm he had total control.
I was meant to be an Olympian

Then, when I was 10 years-old we moved to Bradford and having  had the s*** kicked out of us for the first three months someone else had to take control, enter Jack (shady side). He’s not evil, but he didn’t believe in forever or that everyone has a good side or that disputes can be settled calmly…

Continue reading at:
https://ift.tt/2rGse6N

How I’d educate my child from EYFS through to uni | @DrCWebbBAPhD

This blog post is inspired by a tweet I saw yesterday, which said we should teach our students as we would like our own children to be taught – or something along those lines. This got me thinking how that would go if I could self indulgently plan the monolithic scheme of work and educational settings I’d have my fictitious child go through from EYFS to uni. It’s actually quite a useful exercise to go through as it helps you to unearth some of your own educational values and beliefs if you weren’t that in touch with them already. I’d be interested to read other peoples attempts at such an…

Continue reading at:
https://ift.tt/2IFxGBC