Answered

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

Sagot :

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.

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