Question

if the discriminant is negative how many times will it touch the x axis?

Answer 1

graph of a quadratic function. is it zero?

Answer 2

if the discriminant is negative the solutions are what are called imaginary numbers, so the curve will not touch the x axis.

Answer 3

if discriminant is -ve, it means that f(x)>0 and so at no place f(x)=0 will be satisfied.hence no roots.hence it won't touch x-axis any time :)