MHB Can Absolute Values of Quadratic Functions Determine Their Discriminants?

[Mathick]

Let $$ f(x)$$ and $$ g(x)$$ be quadratic functions such as the inequality $$ \left| f(x) \right| \ge \left| g(x) \right| $$ is hold for all real $$ x$$ . Prove that $$ \left| \Delta_f \right| \ge \left| \Delta_g \right|$$. For quadratic function $$ f(x)=ax^2+bx+c $$, then $$ \Delta=b^2-4ac. $$

I have no idea how I could start this task. Please, help!

 

[Euge]

Hi Mathick,

This was actually a challenge problem that anemone posted http://mathhelpboards.com/challenge-questions-puzzles-28/prove-b-4ac-8804-b-4ac-15129.html. A solution is provided in the last post.