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2. If $\\alpha, \\beta, \\gamma$ solutions for the equation

   math.stackexchange.com/questions/1384996

   Using the root-coefficient relationship, we have the following: $$\alpha + \beta + \gamma = -1,$$ $$\alpha\beta\gamma = -1,$$ $$\alpha\beta + \beta\gamma + \gamma ...

3. Find the cubic whose roots are $\\alpha^3, \\beta^3, \\gamma^3$

   math.stackexchange.com/questions/2285064

   Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

4. If $\\alpha$, $\\beta$ and $\\gamma$ are roots of the following...

   math.stackexchange.com/questions/4983063/if-alpha-beta-and-gamma-are-roots-of...

   (2) $$\frac{\alpha^7+\beta^7+\gamma^7}{7} = \left(\frac{\alpha^5+\beta^5+\gamma^5}{5} \right)\left(\frac{\alpha^2+\beta^2+\gamma^2}{2}\right)$$ I found this interesting problem from a teacher and it got stuck in my head, so if possible I request some hints to solving this problem.

5. polynomials - If $\alpha,\beta,\gamma$ are the roots of...

   math.stackexchange.com/questions/3753474

   Also $\alpha\beta+\beta\gamma+\gamma\alpha=-\alpha\beta\gamma$ so, yes, I can see why you are asking...$\alpha^3+\beta^3+\gamma^3=3\alpha\beta\gamma$ $\endgroup$ – Martin Hansen Commented Jul 11, 2020 at 15:30

6. algebra precalculus - If $\alpha , \beta , \gamma$ are roots of...

   math.stackexchange.com/questions/2519565/if-alpha-beta-gamma-are-roots-of...

   Hints: Note that $\alpha + \beta + \gamma = 0$ ; $\alpha\beta + \alpha\gamma + \beta\gamma = -p $ and $\alpha\beta\gamma = -q $.

7. Minimum of $\\sin \\alpha+\\sin \\beta+\\sin \\gamma$ with...

   math.stackexchange.com/questions/2006243/minimum-of-sin-alpha-sin-beta-sin...

   Find the minimum of $\\sin \\alpha+\\sin \\beta+\\sin \\gamma,$ where $\\alpha,\\beta,\\gamma\\in \\mathbb{R}$ satisfying $\\alpha+\\beta+\\gamma = \\pi$. Options: (a ...

8. Method of moments with a Gamma distribution

   math.stackexchange.com/questions/3104688/method-of-moments-with-a-gamma...

   Based on your expressions for the first and second raw moments, I will assume that the gamma distribution is parametrized by shape α and scale β; i.e., fY(y) = yα−1e−y/β βαΓ(α), y> 0. In such a case, equating on raw (uncentered) sample moments gives the system. y¯1 y¯2 = αβ, =α2β2 + αβ2 = α(α + 1)β2.

9. cubics - Finding the value of...

   math.stackexchange.com/questions/4080197/finding-the-value-of-alpha2-beta-beta...

   Using Vieta's formulas, $$\alpha+\beta+\gamma=\frac{-q}{p}$$ $$\alpha\beta+\beta\gamma+\gamma\alpha=\frac{r}{p}$$ $$\alpha\beta\gamma=\frac{-s}{p}$$ I first thought that this would help. We can find $\alpha\beta\gamma$ by Vieta's formula but the expression inside this bracket could not be possibly found.

10. If $\\alpha, \\beta,\\gamma$ be the roots of $2x^3+x^2+x+1=0$,...

    math.stackexchange.com/questions/3492092

    If $\\alpha, \\beta,\\gamma$ be the roots of $2x^3+x^2+x+1=0$, show that: $$(\\frac{1}{\\beta^3}+\\frac{1}{\\gamma^3}-\\frac{1}{\\alpha^3})(\\frac{1}{\\gamma^3 ...

11. If $α,β,γ$ are the roots of the equation $f(x)=x^3+qx+r=0$ then...

    math.stackexchange.com/questions/4613589/if-α-β-γ-are-the-roots-of-the...

    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 true. It should be obvious to you that your answer is incorrect as you have arrived at a quadratic polynomial, not a cubic.