InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
A certain polynomial `P(x)x in R`when divided by k`x-a ,x-ba n dx-c`leaves remainders`a , b ,a n dc`, resepectively. Then find remainder when `P(x)`is divided by `(x-a)(x-b)(x-c)w h e r eab, c`are distinct. |
|
Answer» By Remainder theorem `f(a)=a,f(b)=b` and `f(c)=c` Let the quotient be `Q(x)` and remainder is `R(x)`. `:.f(x)=(x-a)(x-b)(x-c)Q(x)+R(x)` `:.f(a)=0+R(a)impliesR(a)=a` `f(b)=0+R(b)impliesR(b)=b` and `f(c)=0+R(c)` `impliesR(c)=c` ltbr. So the equation `R(x)-x=0` has there roots a,b and c. But its degree is atmost two. So `R(x)-x` must be zero polynomial (or identity) Hence `R(x)=x`. |
|