If the expression (px^3 + x^2 – 2x – q) is divisible by (x – 1) and (x + 1), then the values of p and q respectively are ? -Maths 9th

If the expression (px^3 + x^2 – 2x – q) is divisible by (x – 1) and (x + 1), then the values of p and q respectively are ? -Maths 9th
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Answer :

Let f(x)=px3+x2−2x−q Since f(x) is divisible by (x−1) and (x+1) so x=1 and −1 must make f(x)=0. Therefore, p+1−2−q=0, i.e., p−q=1; and  −p+1+2−q=0, i.e., p+q=3 Thus p=2 and q=1
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Last Answer : 2x-y=p put x-1,y=-2 =2(1)-(-2)=p p=4

Let us assume that you construct ordered tree to represent the compound proposition (~(p˄q))↔(~p˅~q). Then, the prefix expression and post-fix expression determined using this ordered tree are given as ........... and ............. respectively. (A) ↔~˄pq˅ ~~pq, pq˄~p~q~˅↔ (B) ↔~˄pq˅ ~p~q, pq˄~p~q~˅↔ (C) ↔~˄pq˅ ~~pq, pq˄~p~ ~q˅↔ (D) ↔~˄pq˅ ~p~q, pq˄~p~~q˅↔

Description : Let us assume that you construct ordered tree to represent the compound proposition (~(p˄q))↔(~p˅~q). Then, the prefix expression and post-fix expression determined using this ordered tree are given as ........... and .......... ... ~p~q~˅↔ (C) ↔~˄pq˅ ~~pq, pq˄~p~ ~q˅↔ (D) ↔~˄pq˅ ~p~q, pq˄~p~~q˅↔

Last Answer : (B) ↔~˄pq˅ ~p~q, pq˄~p~q~˅↔