let the equations be x^2+x+2=0 and ax^2+bx+1=0 have atleast one common root then a+b equals to

Asked by sandeepkumarbhadauria41 | 15th Sep, 2021, 02:52: PM

Expert Answer:

Given equations are
 
x2 + x + 2 = 0   ...........................(1)
 
a x2 + b x + 1 = 0  ........................(2)

 
Roots of Eqn.(1) :- begin mathsize 14px style fraction numerator negative 1 plus-or-minus square root of 1 minus 8 end root over denominator 2 end fraction end style 
 
Roots of Eqn.(2)  :-    begin mathsize 14px style space fraction numerator negative b space plus-or-minus space square root of b squared space minus space 4 a end root over denominator 2 a end fraction space end style
if both equations have a common root , then  -b/(2a) = -1/2   or  b = a
 
Also begin mathsize 14px style fraction numerator b squared over denominator 4 a squared end fraction minus 1 over a space equals space minus 7 over 4 end style
if we substitute b =a in above expression, we get a = (1/2) after simplification
 
Hence we have , a = b = 1/2    or  a+b = 1

Answered by Thiyagarajan K | 20th Sep, 2021, 09:50: PM