T:For two given quadratic functions f(x):R=>R and g(x):R=>R where |f(x)|>=|g(x)|, the absolute value of the discriminant of f(x) is not lesser than the absolute value of the discriminant of g(x).
I divided these function into three cases:
1. min(f(x))<0 and min(g(x))<0
2. min(f(x))>=0 and min(g(x))<0
3. min(f(x))>=0 and min(g(x))>=0
In the first case inequation |f(x)|>=|g(x)| is fulfilled only if their zero points are the same. We can deduce from it that if the functions are presented with following pattern: f(x)=ax^2+bx+c anf g(x)=dx^2+ex+f then |a|>=|d| and |a||e|=|d||b| and |a||f|=|d||c| then |b^2+4ac|>=|e^2+4df| because |b^2-4ac|>=|(d^2/a^2)(b^2-4ac)| because d^2/a^2<=1.
In second and third case I haven't come up with any conclusion yet.
I divided these function into three cases:
1. min(f(x))<0 and min(g(x))<0
2. min(f(x))>=0 and min(g(x))<0
3. min(f(x))>=0 and min(g(x))>=0
In the first case inequation |f(x)|>=|g(x)| is fulfilled only if their zero points are the same. We can deduce from it that if the functions are presented with following pattern: f(x)=ax^2+bx+c anf g(x)=dx^2+ex+f then |a|>=|d| and |a||e|=|d||b| and |a||f|=|d||c| then |b^2+4ac|>=|e^2+4df| because |b^2-4ac|>=|(d^2/a^2)(b^2-4ac)| because d^2/a^2<=1.
In second and third case I haven't come up with any conclusion yet.