Mathematics - Quadratic Equation Question with Solution | TestHub

If $\alpha , \beta$ are roots of quadratic equation $5x^2+6x-2=0$

$\Rightarrow 5{\alpha }^2+6\alpha -2=0 \Rightarrow 5{\alpha }^2+6\alpha =2$

$\Rightarrow 5{\beta }^2+6\beta -2=0 \Rightarrow 5{\beta }^2+6\beta =2$

$5S_6+6S_5=5\left({\alpha }^6+{\beta }^6\right)+6\left({\alpha }^5+{\beta }^5\right)$

$={\alpha }^4\left(5{\alpha }^2+6\alpha \right)+{\beta }^4\left(5{\beta }^2+6\beta \right)$

$=2\left({\alpha }^4+{\beta }^4\right)=2S_4$