Let A= { x | x^2 + (m-1)x-2(m+1)=0, x in R} B= { x | ((m-1)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 + (m-1)x-2(m+1)=0 }
We know that
Delta_A = (m-1)^2-4(1)(-2(m+1))
\ \ \ \ \ = m^2-2m+1 + 8m+8
\ \ \ \ \ = (m-3)^2
Delta_A = 0 => m=3 => 1 solution
Delta_A gt 0 => m!=3 => 2 solutions
And for set
B = { x in RR | ((m-1)x^2)+ mx + 1=0 }
Similarly, We know that
Delta_B = m^2-4(m-1)(1)
\ \ \ \ \ = m^2-4m+4
\ \ \ \ \ = (m-2)^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