If-the-equation-p-2-4-p-2-9-x-3-p-2-2-x-2-p-4-p-3-p-2-x-2p-1-0-is-satisfied-by-all-values-of-x-in-0-3-then-sum-of-all-possible-integral-values-of-p-is-fractional-part-fun

Question Number 33944 by rahul 19 last updated on 28/Apr/18

I f the equation

(p^{2} - 4) (p^{2} - 9) x^{3} + [\frac{p - 2}{2}] x^{2} + (p - 4) (p - 3) (p - 2) x + {2 p - 1} = 0 .

is satisfied by all values of x in (0, 3] t h e n

s u m o f a l l p o s s i b l e i n t e g r a l v a l u e s o f

^{'} p^{'} i s ?

{.} = f r a c t i o n a l p a r t f u n c t i o n .

[.] = g r e a t e s t i n t e g e r f u n c t i o n .

Answered by MJS last updated on 28/Apr/18

p \in Z \Rightarrow {2 p - 1} = 0

now {it}^{'} s easy

(p^{2} - 4) (p^{2} - 9) = 0 \Rightarrow p \in {- 3; - 2; 2; 3}

[\frac{p - 2}{2}] = 0 \Rightarrow [\frac{p}{2}] = 1 \Rightarrow p \in {2; 3}

(p - 4) (p - 3) (p - 2) = 0 \Rightarrow {2; 3; 4}

p \in {2; 3}

s u m ({2; 3}) = 5

Commented by rahul 19 last updated on 28/Apr/18

T h a n k y o u s i r!