InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
If m is chosen in the quadratic equation `(m^(2)+1)x^(2)-3x+(m^(2)+1)^(2)=0` such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is(A) `10sqrt5`(B) `8sqrt5`(C) `8sqrt3`(D) `4sqrt3`A. `10sqrt5`B. `5sqrt5`C. `8sqrt3`D. `4sqrt3` |
|
Answer» Correct Answer - B Given quadratic equation is `(m^(2)+1)x^(2)-3x(m^(2)+1)^(2)=0" "…(i)` Let the roots of quadratic Eq. (1)mn are `alpha and beta.` so `alpha+beta(3)/(m^(2)+1)and alphabeta=m^(2)+1` According to the question, the sum of roots is greatest and it is possible only when `(m^(2)+1)` is minimu and minimum value of `m^(2)+1=1,` when `m=0"` `thereforealpha +beta=3` and `alpha beta=1, as m =0` Now, the absolute difference of the cubes of roots `=|alpha^(2)-beta^(3)|` `=|alpha-beta||alpha^(2)+alphabeta|` `=sqrt((alpha+beta)^(2)-4alphabeta)|(alpha+beta)^(2)-alpha beta|` `=sqrt(9-4)|9-1|=8sqrt5` |
|