InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Let a,b,c, `in Riff(x)=ax^(2)+bx+c` is such that a+b+c=3 and `f(x+y)=f(x)+f(y)+xy," for all "x,y inR`, then `sum_(n=1)^(10) f(n)` is equal toA. 330B. 165C. 190D. 225 |
|
Answer» Correct Answer - A We have, `f(x)=ax^(2)+bx+candf(x+y)=f(x)+f(y)+xy`. `:." "f(x+y)=f(x)+f(x)+f(y)+xy" for all "x,y inR` `rArr" "a(x+y)^(2)+b(x+y)+cax^(2)+bx+c+ay^(2)+c+xy" for all "x,y in R`. `rArr" "2axy=cxy" for all "x,yinR` `rArr" "(2a-1)xy-c=0rArra=(1)/(2),c=0` But a+b+c=3 `rArr" "(1)/(2)+b+0=3rArrb=(5)/(2)` `:." "f(x)=ax^(2)+bx+c` `rArr" "f(x)=(1)/(2)x^(2)+(5)/(2)x` Hence, `underset(n=1)overset(10)sumf(n)=(1)/(2)underset(n=1)overset(10)sumn^(2)+(5)/(2)underset(n=1)overset(10)sumn=(1)/(2)xx(10(10+1)(20+1))/(6)+(5)/(2)xx(10(10+1))/(2)=330` |
|