Answer:
[tex]x=4.23[/tex] or [tex]x=-0..23[/tex]
Step-by-step explanation:
Let x be the roots of given equation.
Given.
[tex]x^{2} -4x-1=0[/tex]------------(1)
The standard form of quadratic equation is.
[tex]ax^{2} + bx+c=0[/tex]-------------(2)
We can solve the roots by this quadratic formula
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}[/tex]-----------(3)
We compare the equation 1 and 2.
where [tex]a=1, b=-4, c=-1[/tex]
All values put in the equation 3
[tex]x=\frac{-(-4)\pm\sqrt{(-4)^{2}-4(1)(-1)}}{2(1)}[/tex]
[tex]x=\frac{4\pm\sqrt{16+4}}{2}[/tex]
[tex]x=\frac{4\pm\sqrt{20}}{2}[/tex]
[tex]x=2+\sqrt{5}=4.23\\x=2-\sqrt{5}=-0.23[/tex]
