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.You need to login to perform this action.
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