Question

Write a quadratic equation in the variable x with the solutions √8 and -√7. 0= _______

Answer 1

The roots of the quadratic equation are:

`\alpha=\sqrt[]{8}\text{ and }\beta=-\sqrt[]{7}`

Any quadratic equation with alpha and beta as the roots is given by:

`x^2-(\alpha+\beta)x+\alpha\beta=0`

Substitute the values to get:

`\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}`

The above equation is the quadratic equation for the roots given in the question.