Solving a quartic equation with parameters

This video is about an equation with a parameter. Two methods are shown.
If you need to post a picture of your solution or idea:
#ChallengingMathProblems #FactoringPolynomials

[itisi]

The method I used to solve this was to first rewrite it as a quadratic in a. Then, I factorised the (x^4 - 2x^2 + x) into x(x - 1)(x^2 + x - 1). third, I noticed that if I could get a pair of factors of that expression to sum to (2x - 1), the a term, I could factorise the whole thing using that, and found that (x^2 + x - 1) - (x^2 - x) = 2x - 1. from this, I factorised the equation into (a - x^2 + x)(a + x^2 + x - 1), leading to the 2 final equations giving the same answers you solved for.

I really enjoyed this parametric equation, as I haven't encountered many problems of this type so it was something relatively new to me and gave me a great challenge. Love your content and the mental stimulation and learning I get from it, I have already developed a lot of skill and learned many techniques from this channel!

[SyberMath]

I like this video because at first glance it looks quite complicated but when you realize you can write it as a quadratic, it becomes somewhat easier. The solution takes us through different manipulations and we arrive at the answer. Any thoughts?

[endormaster]

I've learnt so much here, thank you

[scottleung]

Interesting - I was actually able to find a explicitly before getting the solutions for x. I think that's fine, since the quadratics add up with mine at the end.

[mohamedfarouk]

Thank you! Btw why did you stop making calculus videos? They were very helpful.

[mevludezirek]

Harika bir video olmuş 😊 Emeğinize sağlık

[aashsyed]

THE WAY YOU SPOKE QUARTIC WAS CORTEK IN SUBTITLES #FUNNY

[asmocak]

Kombinatorik problemleri gelecek video planlariniz arasinda var mi?