Question 76796
The given equation is:


{{{ y = x^2  - 7x  + 11 }}} 


To find the x-intercepts we substitute y = 0, which then gives us a quadratic in x. 


That is {{{x^2 - 7x + 11 = 0 }}}


This can be solved by using the quadratic formula. 


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 


Substittuting for the values, we get: 


{{{x = (7 +- sqrt( 7^2 - 4*(1)*(11)))/(2*1)}}} 


{{{x = (7 +- sqrt(49 - 44)/2)}}}


{{{x = ( 7 +- sqrt(5)/2)}}} 


Hence, the x intercepts are: 



{{{x = (7 + sqrt(5))/2) }}} and {{{x = (7 - sqrt(5))/2) }}} 



Hence, the solutions.