A student notices that the roots of the equation `x^(2)+bx+a=0` are each 1 less than the roots of the equation `x^(2)+ax+b=0`. Then a+b is.

Options

A. Possibly any real number
B. -2
C. -4
D. -5

Answer

C

Explanation

`alpha + beta=-b` and `alpha beta = a`
`alpha +1+ beta +1=-a rArr alpha + beta+2=-a rArr -b +2=-a`
`b-a=2 " " ....(1)`
`(alpha +1)(beta+1)=b rArr alpha beta+ alpha+beta+1=b rArr a+(-b)+1=b`
`2b-a=1" " ....(2)`
from (1) & (2), b=-1, a=-3, a+b=-4