A) \[-2\le m\le 1\]
B) \[-1\le m\le 1\]
C) \[2<m<3\]
D) none of these
Correct Answer: A
Solution :
Key Idea: If roots are real, then discriminant \[D\ge 0.\] Given equation is \[m\,{{x}^{2}}-4x+2(m+1)=0.\] Since, the roots are real \[\therefore \] \[{{b}^{2}}-4ac\ge 0\] \[\Rightarrow \]\[16-4.m.2(m+1)\ge 0\] \[\Rightarrow \]\[2-{{m}^{2}}-m\ge 0\] \[\Rightarrow \]\[{{m}^{2}}+m-2\le 0\] \[\Rightarrow \]\[(m+2)(m-1)\le 0\] \[\Rightarrow \]\[-2\le m\le 1\] Note: If the roots are imaginary, then discriminant,\[D<0.\]
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