$ax^2 +bx +cm =0$ , $bx^2 + cx +am =0$ and $cx^2 + ax +bm=0$ are three quadratic equations in $x$ , $a,b ,c$ are real numbers and $m$ is a positive real , find the possible numerical values of $m$ so that atleast one of these equations has a real root.
How do I attempt such a question? What is the intuition behind this?
I don't get where to start. Can someone help me out?
I got $b^2 \ge 4acm$, $c^2 \ge 4abm$, $a^2 \ge 4bcm$ but what do I do with these? Atleast one of them has to be true? Is there something else I should try?
Thanks in advance.