The solution set of the given quadratic equation is:
[tex]x=\sqrt{5}\ and\ x=-\sqrt{5}[/tex]
We are given a quadratic equation in terms of the variable ''x'' as:
[tex]x^2-5=0[/tex]
Now we are asked to find the roots of this polynomial equation.
on adding both side of the equation with 5 we get,
[tex]x^2-5+5=0+5\\\\x^2=5[/tex]
Now on taking the square root on both the side we get:
[tex]x=\pm \sqrt{5}[/tex]
Hence, the roots are:
[tex]x=\sqrt{5}[/tex] and [tex]x=-\sqrt{5}[/tex]