If α, β are the roots of x^2+p x-q=0 and γ, are roots of x^2-p...

\because \alpha, \beta$are the roots of$x^2+p x-q=0\therefore \alpha+\beta=-p and \alpha \times \beta=-q\gamma, \delta$are roots of$x^2-p x+r=0\gamma, \delta$are roots of$x^2-p x+r=0\therefore \gamma+\delta=+p and \gamma \times \delta=r(\beta+\gamma)(\beta+\delta)=\beta^2+\beta \delta+\beta \gamma+\delta \gamma=q+r \left[\because \beta\right.is the root of \left.x^2+p x-q=0 \quad \therefore \beta^2+ p \beta=q\right]