The inequality of p

Solution follows here:

^{2}+5 < 5p + 14 can be satisfied if :
(A) p
<= 6, p = -1

(B) p
= 6, p=-2

(C) p
<= 6, p <= -1

(D) p
>= 6, p = 1Solution follows here:

__Solution:__

This
can be done quickly by eliminating options by substitution method:

All
the options centre around 6.

Check
out for p=6, 6

^{2}+5 < 5(6)+14 => 41 < 44 True
Check
out for p=5<6, 5

^{2}+5<5(5)+14 => 30<39 True
Check out for p=7>6, 7

^{2}+5<5(7)+14 => 54<49 False hence option D is out
Check out for p=-2<-1, (-2)

^{2}+5<5(-2)+14 => 9<4 False hence options B and C are out
The only left out option is A

Answer is (A)
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