Find the roots of the quadratic equations by using the quadratic formula in each of the following
`1/2 x^(2)-sqrt(11)x+1=0`

Explanation

Given equation is `1/2 x^(2)-sqrt(11)x+1=0`
on comparing with `ax^(2)+bx+c=0` we get
`a=1/2,b=-sqrt(11)` and `c=1`
`:.` By quadratic formula `x=(-b+-sqrt(b^(2)-4ac))/(2a)`
`=(-(-sqrt(11))+-sqrt((-sqrt(11))^(2)-4xx1/2xx1))/(2(1/2))`
`=(sqrt(11)+-sqrt(11-2))/1=sqrt(11)+-sqrt(9)`
`=sqrt(11)+-3=3+sqrt(1),sqrt(11)-3`
So `3+sqrt(11)` and `sqrt(11)-3` are the roots of the given equation.