How to solve cubic vector equation?
A cubic equation $$x^3+ax^2+bx+c=0$$ has three solutions, which can be found analytically. Likewise, a vector equation like $$underline{underline{A}} underline{x} +...
View Article“Factorizations” of $a^3+b^3+c^3+mabc$?
It is easy to see that $$a^2+b^2+c^2+ab+bc+ca=frac{1}{2}((a+b)^2+(b+c)^2+(c+a)^2),$$ $$a^2+b^2+c^2+2(ab+bc+ca)=(a+b+c)^2,$$ $$a^2+b^2+c^2-ab-bc-ca=frac{1}{2}((a-b)^2+(b-c)^2+(c-a)^2),$$ and moreover,...
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Finding cubic bezier curve endpoints based on relationship between endpoints...
I have the following information about a bezier curve: The curve begins at $x=0$ and ends at $x=1$. The curve has two control points each at the same height as their closest endpoints, one at $x=.25$...
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How to find a perfect regression fit in R?
I have a set of points, which I know can be described with some equation. How can I find this equation? The scatter plot for this set looks like this: I look at the plot and assume that I can use a...
View ArticleApplications of the formula expressing roots of a general cubic polynomial
I know that the mathematics related to finding the general formula by expressing the roots of a third (and fourth) degree polynomial by means of radicals has had an impressive impact on mathematics...
View ArticleFind the natural cubic spline function whose knots are $-1$, $0$, and $1$ and...
Find the natural cubic spline function whose knots are $-1$, $0$, and $1$ and that takes the values $S(-1)=13$, $S(0)=7$, and $S(1)=9$. I’m not sure how to go about this. Any solutions/hints are...
View Articlecoefficient of a cubic expression
So the given cubic is $x^3-2x^2+ax+10=0$ . The condition is one of the root is additive inverse of another. I need to find the coefficient $a$ . I did some algebraic calculations and cancelling of the...
View ArticleHaving trouble finding roots/factorizing a cubic equation
I’ve been trying to find a method that can work for any cubic equation, but I can’t seem to find one. Right now, I’m trying to find the roots/ factorize the following equation: $x^3-5x^2+3x+9 = 0$....
View ArticleShow that the difference between the greatest and the least of them is not...
Let the roots of the cubic equation $x^3+ax^2+bx+c=0$ be real.Show that the difference between the greatest and the least of them is not less than $sqrt{a^2-3b}$ nor greater than $2sqrt{a^2-3b}$. Let...
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Find the Cubic equation given 1 Point and Slope
The question asks to find a cubic equation given point A (0/18) slope here is 0. Point B only given the x=20 and slope is -0.6. Please help, been trying to solve it for so long now. 1.)...
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