If $α,β,γ$ are the roots of the equation $f(x)=x^3+qx+r=0$ then …
Jan 8, 2023 · It’s not clear why you have written $$\frac {\gamma^2-2\alpha\beta} {\gamma^2}=\frac {1-2\alpha\beta\gamma} {\gamma^2\gamma}$$ This would mean that …
Minimum of $\\sin \\alpha+\\sin \\beta+\\sin \\gamma$ with …
Nov 9, 2016 · @DarshitSharma We are not given that $\alpha$, $\beta$, and $\gamma$ are the angles of a triangle, they are real numbers which sum to $\pi$. So we cannot directly apply …
Find a new cubic equation with new roots $\alpha\beta$, …
Jul 12, 2019 · However, this method is quite tedious, especially if the new roots are $\alpha+\beta$, $\beta+\gamma$ and $\gamma+\alpha$. So does substitution method exist …
Let $\\alpha$ and $\\beta$ be the roots of an quadratic equation …
Dec 3, 2024 · $\beta= \dfrac {-p-\sqrt {p^2-4q}} {2}$ and i did the same for the other equation and replaced these values for $\alpha,\beta,\gamma$ and $\delta$ but the equation became too …
Find the cubic whose roots are $\alpha^3, \beta^3, \gamma^3$
May 17, 2017 · Basically, I know I've to find what's the value of $\alpha^3+\beta^3+\gamma^3$, $\alpha^3\beta^3+\alpha^3\gamma^3+\beta^3\gamma^3$ and $\alpha^3\beta^3\gamma^3$. …
If $α, β, γ$ are roots of $x^3 - x -1 = 0$, then find the value of ...
Jun 28, 2018 · Then $\alpha'$, $\beta'$, and $\gamma'$ are roots of this polynomial, and if you have the three roots of a polynomial you should know how to find their sum...
relation between roots and coefficient in a cubic polynomial
Dec 24, 2021 · If $\alpha,\beta,\gamma$ are roots of the cubic equation $$2x^ {3}+3x^2-x-1=0$$ then I want to find the equation whose roots are $\frac {\alpha} {\beta+\gamma}, \frac {\beta} …
geometry - How to find three angles of a point in 3D.
Apr 14, 2018 · Suppose angle of vector related to x axis is $\alpha$, related to y axis is $\beta$ and related to z axis is $\gamma$ then we have: Due to presumption; $\sqrt {a^2+b^2+c^2}=1$
Prove that $\mathbb {Q} (\alpha, \beta, \gamma, r_1) = \mathbb …
Nov 29, 2025 · 2 One can check that: $$\frac {- (a \gamma -2 c )\, r_1+ 2 \gamma ^2-2b \gamma+a c} { (4\gamma +a^2 -4 b)\, r_1+ (a \gamma - 2 c)}=r_4$$ where we recall that …
Find the cubic equation of roots $α, β, γ$.
Jul 7, 2015 · The two applications of Vieta's Formulas above expressions all of these coefficients in terms of symmetric functions of the roots $\alpha, \beta, \gamma$, so the coefficients can …