A) 4
B) 1
C) 2
D) None of these
Correct Answer: A
Solution :
Idea Here, ax2 + bx + c = 0 has roots \[\alpha \] and \[\beta \]\[\alpha +\beta =\frac{-b}{a},\alpha \beta =\frac{c}{a}\] If roots are reciprocal to each other i.e., \[\alpha ={{\alpha }_{1}}\]\[\beta =\frac{1}{a}\Rightarrow \frac{c}{a}=1\Rightarrow c=a\] We have given the equation as \[({{m}^{2}}-3){{x}^{2}}+3mx+3m+1=0\] \[\because \]Roots are reciprocal to each other \[\therefore \] \[\alpha \beta =1\] \[\Rightarrow \] \[\frac{c}{a}=1\Rightarrow \frac{3m+1}{{{m}^{2}}-3}=1\] \[\Rightarrow \] \[3m+1={{m}^{2}}-3\] \[\Rightarrow \] \[{{m}^{2}}-3m-4=0\] \[\Rightarrow \] \[{{m}^{2}}-4m+m-4=0\] \[\Rightarrow \] \[m(m-4)+1(m-4)=0\] \[\Rightarrow \] \[(m-4)(m+1)=0\] \[\Rightarrow \] \[m=4,-1\] TEST Edge Application of quadratic equation based questions are asked. To solve such type of question, students are advised to understand the concept of quadratic equation.
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