If $\alpha$, $\beta$, $\gamma$ are the three roots of the cubic function, $ x^3-2x^2-4x=5$, find the value of β + + β. I know that there is a way to calculate the $\alpha \beta + \alpha \gamma + \beta \gamma$ with something that uses $\alpha + \beta + \gamma$ or $\alpha\beta\gamma$ but I can't find that.
cubic function, $ x^3-2x^2-4x=5$
-1
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functions
polynomials
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6Try expanding the expression $(x - \alpha) (x - \beta) (x-\gamma)$ and then comparing coefficients with $x^3-2x^2-4x-5$. – 2017-02-07
1 Answers
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$\alpha$, $\beta$, $\gamma$ satisfies $$x^3-2x^2-4x-5=0$$
Using Vieta's Formula, we know that $$\alpha \beta +\beta \gamma+\gamma \alpha= -4$$ As $-4$ is the coefficient of $x$. So we are done.