Question
Sun March 08, 2015 By: Varsha Mittal

If a and b are the roots of the equation x^2+3x+4=0, then find the equation whose roots are a+1 and b+1

Expert Reply
Prasenjit Paul
Sun March 08, 2015
x squared plus 3 x plus 4 equals 0 S u m space o f space t h e space r o o t s space o f space t h e space e q u a t i o n comma space a plus b equals negative 3 P r o d u c t space o f space t h e space r o o t s space o f space t h e space e q u a t i o n comma space a b equals 4 I f space left parenthesis a plus 1 right parenthesis space a n d space left parenthesis b plus 1 right parenthesis space a r e space t h e space r o o t s space o f space t h e space e q u a t i o n space t h e n  S u m space o f space t h e space r o o t s comma left parenthesis a plus 1 right parenthesis plus left parenthesis b plus 1 right parenthesis equals left parenthesis a plus b right parenthesis plus 2 equals negative 3 plus 2 equals negative 1 P r o d u c t space o f space t h e space r o o t s comma left parenthesis a plus 1 right parenthesis left parenthesis b plus 1 right parenthesis equals a b plus a plus b plus 1 equals 4 minus 3 plus 1 equals 2  T h e space e q u a t i o n space w i l l space b e x squared plus left parenthesis a plus 1 plus b plus 1 right parenthesis x plus left parenthesis a plus 1 right parenthesis left parenthesis b plus 1 right parenthesis equals 0 x squared minus x plus 2 equals 0
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