Shall we use Newton's Sum?
Algebra
Level
5
Consider the cubic equation, \( 2x^3 - 7x^2 + 10x - 6 = 0 \).
The roots of the above cubic equation are \( \alpha , \beta , \gamma \). If,
\[ \displaystyle\sum_{r=1}^{10} [ \alpha^{r} + \beta^{r} + \gamma^{r} ] = \dfrac{m}{n}, \]
where \(m\) and \(n\) and coprime positive integers,
then find \( m + n \).
by
Kunal Joshi