Let #A= { x  x^2 + (m1)x2(m+1)=0, x in R}# #B= { x  ((m1)x^2)+ m x +1=0, x in R}# Number of values of #m# such that #A uu B# has exactly 3 distinct elements, is? A) 4 B) 5 C) 6 D) 7
1 Answer
Consider the set
#A = { x in RR  x^2 + (m1)x2(m+1)=0 }#
We know that
# Delta_A = (m1)^24(1)(2(m+1)) #
# \ \ \ \ \ = m^22m+1 + 8m+8 #
# \ \ \ \ \ = (m3)^2 #
# Delta_A = 0 => m=3 => 1 # solution
# Delta_A gt 0 => m!=3 => 2 # solutions
And for set
# B = { x in RR  ((m1)x^2)+ mx + 1=0 }#
Similarly, We know that
# Delta_B = m^24(m1)(1) #
# \ \ \ \ \ = m^24m+4 #
# \ \ \ \ \ = (m2)^2 #
# Delta_B = 0 => m=2 => 1 # solution
# Delta_B gt 0 => m!=2 => 2 # solutions
Now we want

One element from A, two elements from B:
#=> Delta_A=0, Delta_B gt 0#
#=> (m =3) nn (m!=2) => m= 3# 
One element from B, two elements from A
# => Delta_B=0, Delta_A gt 0#
#=> (m =2) nn (m!=3) => m= 2#
Therefore there are