The roots of the quadratic equation are:
[tex]\alpha=\sqrt[]{8}\text{ and }\beta=-\sqrt[]{7}[/tex]Any quadratic equation with alpha and beta as the roots is given by:
[tex]x^2-(\alpha+\beta)x+\alpha\beta=0[/tex]Substitute the values to get:
[tex]\begin{gathered} x^2-(\sqrt[]{8}-\sqrt[]{7})x+(\sqrt[]{8})(-\sqrt[]{7})=0 \\ x^2-\sqrt[]{8}x+\sqrt[]{7}x-\sqrt[]{56}=0 \end{gathered}[/tex]The above equation is the quadratic equation for the roots given in the question.
