question_answer

    The roots of the equation\[\left| \begin{matrix}    1 & 4 & 20  \\    1 & -2 & 5  \\    1 & 2x & 5{{x}^{2}}  \\ \end{matrix} \right|=0\]are

A)  \[-1,-2\]                             

B)  \[-1,2\]

C)  \[1,-2\]                               

D)  \[1,2\]

Correct Answer: B

Solution :

                Since,\[\Delta SPM\]is an equilateral triangle. Therefore, \[SP=PM=SM\] \[\therefore \]                  \[\angle PMZ=90{}^\circ \] and        \[\angle PMS=60{}^\circ \] \[\therefore \]                  \[\angle SMZ=30{}^\circ \] Now, in right angle\[\Delta SMZ\]                 \[\sin 30{}^\circ =\frac{SZ}{SM}\] \[\Rightarrow \]               \[\frac{1}{2}=\frac{2a}{SM}\] \[\Rightarrow \]               \[SM=4a\] \[\Rightarrow \]               \[PM=4a\]               \[(\because PM=SM)\]