Lösung 2.3:9b

Aus Online Mathematik Brückenkurs 1

The points of intersection are those points on the curve which also lie on the  x -axis, i.e. they are those points which satisfy both the equation of the curve y=x2−5x+6 and the equation of the  x -axis y=0,

y=x2−5x+6y=0 

This system of equations gives directly that y=0 and that  x must satisfy the second-order equation x2−5x+6=0 . By completing the square, we obtain that the left-hand side is

x2−5x+6=x−252−252+6=x−252−425+424=x−252−41

and this gives that the equation has solutions

x=2521, i.e. x=25−21=24=2 and x=25+21=26=3.

The intersection points are therefore 20  and 30 .