• # question_answer If (m3 - 3) x2 + 3mx + 3m +1=0 has roots which  are reciprocal of each other, then the value of m can be A)  4                                             B)  1                     C)  2                                             D)  None of these

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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