Question

A root of x2 – 5x – 1 = 0 is

Answer 1

The roots are
`(5+√(29))/(2)` and
`(5-√(29))/(2)`

Step-by-step explanation:

The general form of the quadratic equation is:

ax² + bx + c = 0

The given equation is:

x² - 5x - 1 = 0

By comparison:

a = 1

b = -5

c = -1

To get the roots of the equation, we will use the quadratic formula shown in the attached image.

This means that:

either
`x = (5+√((-5)^2-4(1)(-1)))/(2(1)) = (5+√(29))/(2)`

or
`x = (5-√((-5)^2-4(1)(-1)))/(2(1)) = (5-√(29))/(2)`

Hope this helps :)

Answer 2

`x^2-5x-1=0\\\\ a=1,\ b=-5,\ c=-1\\\\ \Delta=b^2-4ac=(-5)^2-4*1*(-1)=25+4=29\\\\ √(\Delta)=√(29)\\\\ x_1=(-b-√(\Delta))/(2a)=(-(-5)-√(29))/(2*1)=(5-√(29))/(2)\\\\ x_2=(-b+√(\Delta))/(2a)=(-(-5)+√(29))/(2*1)=(5+√(29))/(2)\\`