Shall we use Newton's Sum?

Algebra Level 5

Consider the cubic equation, 2x37x2+10x6=0 2x^3 - 7x^2 + 10x - 6 = 0 .

The roots of the above cubic equation are α,β,γ \alpha , \beta , \gamma . If,

r=110[αr+βr+γr]=mn, \displaystyle\sum_{r=1}^{10} [ \alpha^{r} + \beta^{r} + \gamma^{r} ] = \dfrac{m}{n}, where mm and nn and coprime positive integers,
then find m+n m + n .

×

Problem Loading...

Note Loading...

Set Loading...