Quartic Equations Part 1

[@holyshit922]

You can use Horner scheme to get y^4+py^2+qy+r=0 equation

[@dkiproch]

is it possible to solve any quartic equation using this method?

[@holyshit922]

Yes, moreover reducing to the form y^4+py^2+qy+r=0 is not necessary Reducing quartic to the form y^4+py^2+qy+r=0 is helpful when you compare quartic to the product of two quadratics written using undetermined coefficients

[@michaelrosen4916]

Thank you for explaining the substitutions, really helpful.

[@calvinjackson8110]

All of this song and dance could be completely cut out if you used the substitution x = y - (a/4). It gives the desired form the FIRST time!

[@mariomario-ih6mn]

Nice video I didn’t get really understand your video when I was 11 now I’m 13 and I fully understand it.

[@heavennoes]

cool, I'm 10 and I'm here to see what I can do.

[@mariomario-ih6mn]

@@heavennoes I turned 14 now

[@holyshit922]

Try to reduce general quartic in x to quadratic in y^2 I tried and got sextic which is difficult to solve for me

[@finnboltz]

How did you do it?

[@holyshit922]

@@finnboltz a_{4}x^4+a_{3}x^3+a_{2}x^{2}+a_{1}x+a_{0} = 0 Let x = (pt+q)/(t+1) Equate coefficients of t^3 and t to zero You will have 10th degree polynomial but P(t) = a_{4}p^4+a_{3}p^3+a_{2}p^{2}+a_{1}p+a_{0} is factor of this polynomial so after division I reduced resolving equation to 6th degree equation but i am unable to solve this sextic equation Resolving equation is sextic in p

[@jonjonmia]

Can someone help me find the general formula for q?????? given p=-3a^2)/8 + b

[@bobbyheffley4955]

[(a^3)-4ab+8c]/8

[@cameronspalding9792]

I think your missing a +y^4

[@grankoczsk]

He cancelled them out

[@kawawashaibu6854]

Sante

[@kjchung9230]

this get even complicated!!

[@elliotnicholson5117]

Sorry :) I hope it isn’t too difficult to follow.

[@Anonymous-wj6bu]

Solving quartic equations involve a lot of algebraic manipulations so I don’t know see how it could be less complicated

[@alvarolealjr]

thank you for trying ..

[@Superpaul205]

Alvaro Leal what do you mean