Question

Which of the following represents all solutions of x² - 4x-1=0?

Answer 1

`x=4.23` or
`x=-0..23`

Explanation:

Let x be the roots of given equation.

Given.

`x^(2) -4x-1=0`------------(1)

The standard form of quadratic equation is.

`ax^(2) + bx+c=0`-------------(2)

We can solve the roots by this quadratic formula

`x=\frac{-b\pm\sqrt{b^(2)-4ac}}{2a}`-----------(3)

We compare the equation 1 and 2.

where
`a=1, b=-4, c=-1`

All values put in the equation 3

`x=\frac{-(-4)\pm\sqrt{(-4)^(2)-4(1)(-1)}}{2(1)}`

`x=(4\pm√(16+4))/(2)`

`x=(4\pm√(20))/(2)`

`x=2+√(5)=4.23\\x=2-√(5)=-0.23`