Q) If a x squared plus b x plus 10 equals 0 space d o e s space n o t space h a v e space t w o space d i s t i n c t space r e a l space r o o t s space t h e n space t h e space p o s s i b l e space v a l u e s space o f space 5 a plus b space a r e space left parenthesis a comma b element of space R space comma space a not equal to 0 right parenthesis space
left parenthesis A right parenthesis minus 3 space space space space space left parenthesis B right parenthesis minus 2 space space space left parenthesis C right parenthesis minus 1 space space space left parenthesis D right parenthesis 0
 

Asked by araima2001 | 6th Apr, 2017, 06:25: AM

Expert Answer:

begin mathsize 16px style Given space that space ax squared plus bx plus 10 equals 0 space does space not space have space two space distinct space real space roots.
This space means space roots space are space equal.
condition space for space the space equal space roots space is space straight b squared minus 4 ac equals 0
Here comma space straight c equals 10.
rightwards double arrow straight b squared minus 40 straight a equals 0
rightwards double arrow straight b squared equals 40 straight a
rightwards double arrow straight a equals straight b squared over 40 space space space space.... left parenthesis straight i right parenthesis
To space find space possible space values space of space 5 straight a plus straight b comma
straight f equals 5 straight a plus straight b
straight f equals 5 cross times straight b squared over 40 plus straight b space space space space space.... From space left parenthesis straight i right parenthesis
straight f equals straight b squared over 8 plus straight b
straight f apostrophe equals straight b over 4 plus 1
then space straight f apostrophe equals 0
straight b over 4 plus 1 equals 0
straight b equals negative 4
straight a equals straight b squared over 40 equals 16 over 40 equals 2 over 5
straight f apostrophe apostrophe equals 1 fourth greater than 0
straight f space has space minima.
Value space of space 5 straight a plus straight b equals 5 cross times 2 over 5 minus 4 equals negative 2


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Answered by Sneha shidid | 6th Apr, 2017, 10:12: AM