Question

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

Answer 1

Answer:

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

Step-by-step 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

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

$x=\frac{4\pm\sqrt{16+4}}{2}$

$x=\frac{4\pm\sqrt{20}}{2}$

$x=2+\sqrt{5}=4.23\\x=2-\sqrt{5}=-0.23$