Question

can a curve of a quadratic polynomial meet x axis at two points

Answer 1

it not not necessarily that curve of a quadratic polynomial meet x axis at two points

it may meet at no points (when it have no real solution )(D<0)

or may meet at only at one point (when it have identical solutions)(D=0)

or may meet at two points (when have two distinct solution )(D>0)

Answer 2

,a quadratic polynomial meets x-axis 
1)at two points if it has 2 real roots
2)at one point if it has 1 real and 1 complex root
3)never meets x-axis if it has two complex roots