Question

What is the root of f(x) =-x^2 - 3x - 1

Answer 1

`x = ( -3 - √(5) )/(2) \: or \: x = ( -3 + √(5) )/(2)`

Explanation:

The given function is

`f(x) = - {x}^(2) - 3x - 1`

To find the roots, we solve:

`- {x}^(2) - 3x - 1 = 0`

Multiply through by -1 to get:

`{x}^(2) + 3x + 1 = 0`

We compare to the general quadratic equation

`a {x}^(2) + bx + c = 0`

Then we have a=1,b=3, c=1.

The solution is given by:

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

`x = \frac{ - 3\pm \sqrt{ { (- 3)}^(2) - 4 *1 * 1 } }{2 * 1}`

`x = ( - 3\pm √( 9 - 4 ) )/(2)`

`x = ( -3\pm √(5) )/(2)`

`x = ( -3 - √(5) )/(2) \: or \: x = ( -3 + √(5) )/(2)`