Question 1090564
{{{g(x)=x^2-3x+4}}}...this is quadratic function, and it may have one, two, or zero roots

The discriminant {{{b^2-4*a*c}}} is important because it tells you how many roots a quadratic function has.  

1. {{{b^2-4*a*c<0}}} There are {{{no}}}{{{ real}}} roots.(there will two complex roots) 

2. {{{b^2-4*a*c=0}}} There is {{{one}}}{{{ real}}} root.

3. {{{b^2-4*a*c>0}}} There are {{{two}}}{{{ real}}} roots. 


 in your case {{{b^2-4*a*c=(-3)^2-4*1*4=-7}}} => {{{b^2-4*a*c<0}}} and there is {{{no}}}{{{ real}}} roots (there will two complex roots) 

check using quadratic formula:

{{{g(x)=x^2-3x+4}}}

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

{{{x = (-(-3)+- sqrt( (-3)^2-4*1*4 ))/(2*1) }}}

{{{x = (3+- sqrt( 9-16 ))/2 }}}

{{{x = (3+- sqrt( -7 ))/2 }}}

{{{x = (3+- i*sqrt( 7 ))/2 }}}

complex solutions:

{{{x = 3/2+ i*sqrt( 7 )/2 }}}

{{{x = 3/2- i*sqrt( 7 )/2 }}}