If $α,β,γ$ are the roots of the equation $f(x)=x^3+qx+r=0$ then find ...
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 $\gamma^3=1$, which is not …
Let $\\alpha$ and $\\beta$ be the roots of an quadratic equation $x^2 ...
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 complex …
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 $\alpha^3\beta^3\gamma^3$. But I m …
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 Jensen's …
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 for this condition or is the …
geometry - How to find three angles of a point in 3D. - Mathematics ...
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; $\sqrt {a^2+b^2+c^2}=1$
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} …
polynomials - If $\alpha,\beta,\gamma$ are the roots of $x^3+x+1=0 ...
Jul 11, 2020 · I think your approach is pretty straightforward and thus the quickest (you may have to think for other approaches, it takes time)). Also as $x^3=-x-1$ for $\alpha,\,\beta,\,\gamma$ you …
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 be related …
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...