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.

you seem like you are missing something or we are unsure about something.

look please this example :

x^{2 }+ 4 = ax^{2 }+bx +c , there a = 1 ( > 0 ) ( b= 0 no problem) and c= 4 , ∆ < 0 ( ∆ = - 16) (as you would) then look at the solution

x_{1}= (-b +√ ∆)/2 x_{2} = (-b -√ ∆)/2

x_{1 }= 2i x_{2} = - 2i both x_{1 }& x_{2 }ϵ ₵

and how did you compare with zero ?

( when you say x_{1 },x_{2 }are >0 ??)