Tagged Questions
0
votes
1answer
21 views
Relationship between 2 Dimensional Quadratic systems and roots
Given four points
$(x_1, y_1)
(x_2, y_2)
(x_3, y_3)
(x_4, y_4)$
How does one construct a system of two equations:
$a_1x + a_2x^2 + a_3y + a_4y^2 + a_5xy = c_1$
$b_1x + b_2x^2 + b_3y + b_4y^2 + ...
3
votes
4answers
113 views
Solving this 3-degree polynomial
I'm trying to factor the following polynomial by hand:
$-x^3 + 9x^2 - 24x + 20 = 0$
The simplest I could get is:
$-x^2(x-9) - 4(5x+5) = 0$
Any ideas on how I could go ahead and solve this by hand? ...
14
votes
2answers
456 views
Find all roots of $\,(x + 1)(x + 2)(x + 3)^2(x + 4)(x + 5) = 360$
The question is to find all complex roots of
$$(x + 1)(x + 2)(x + 3)^2(x + 4)(x + 5) = 360$$
and it is meant to be solved by hand.
Is there any quick way to solve this using some trick that I'm not ...
0
votes
1answer
82 views
How to solve for x
$W(4d^2 (1-x^2)^2) = abc^3x \sqrt{(\pi^2 (i-x^2)^2 + 16 x^2) }$
I have to find x ,i have the values of all other constants ,
I tried to separate it using partial fraction but I am stuck.
a=3
b=4
c=7
...
1
vote
3answers
117 views
Adjunction of a root to a UFD
Let $R$ be a unique factorization domain which is a finitely generated $\Bbbk$-algebra for an algebraically closed field $\Bbbk$. For $x\in R\setminus\{0\}$, let $y$ be an $n$-th root of $x$. My ...
