Question

. What are the exact solutions of x2 - x - 4 = 0?

Answer 1

`x=(1+√(17))/(2)` and
`x=(1-√(17))/(2)`

Explanation:

`x^2 - x - 4 = 0`

To solve for x , apply quadratic formula

`x=(-b+-√(b^2-4ac))/(2a)`

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

Plug in all the values in the formula

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

`x=(1+-√(1+16))/(2)`

`x=(1+-√(17))/(2)`

`x=(1+√(17))/(2)` and
`x=(1-√(17))/(2)`

Answer 2

x ² - x - 4 = 0

`x_(1) = (1+ √(1+16) )/(2)= (1+ √(17) )/(2) = 2.56`

`x_(2) = (1- √(17) )/(2)= - 1.56`
Exact values are x 1 = 2.56 and x 2 = -1.56