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 > 0.

This is possible only when either both terms are (+)ve or both (–)ve.

(yc) (yb) = (+)ve, when y > c and y > b

(yc) (yb) = (–)ve, when y < c and y < b

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

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