O.J

Hi I'm trying to solve this : assume: a*x^2+b*x+c>=0 for all x with a≠0 then have: b^2-4*a*c<=0 but I couldn't. I proved it when the quadratic equation is greater than zero a*x^2+b*x+c>0 for all x with a≠0 but not for greater then or equal to zero. So any one help in solving this please.