Show that if x is real , the expression x2-bc/ 2x-b-c has no real value between b and c.

As x is real, so D $\ge$ 0.

$\Rightarrow \mathrm{y} \in (-\infty , \mathrm{b}] \cup [\mathrm{c}, \infty ) \left[\mathrm{assuming} \mathrm{that} \mathrm{b} <\hspace{0.17em}\mathrm{c}\right]$

Hence, the given expression has no real value between b and c.