Question

I tried doing this problem and this is the problem

if $a, b,$ and $c$ are real numbers and $a+bx+cx^2 \geq 0$ for any real number $x$, explain why $b^2-4ac \leq 0$

this is how i am trying to do if we know $a +bx+cx^2 \geq 0$ then our disriminant is $\sqrt{b^2 - 4ca}$ but this cant be $\leq o$ because it would make our square root negative. and that woulnd exist so the solution wouldnt exist.

I am confused on this please help out, if you could give me some hints or a solution i would be happy, these are just practice questions i need help on

Answer 1

instead of using $$
use \[ \]

Answer 2

alright thankss ill repost again