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# The pair of lines represented by $3ax^2+5xy+(a^2-2)y^2=0$ are perpendicular to each other for

$\begin{array}{1 1}(A)\;\text{two value of a}\\(B)\;\forall a\\(C)\;\text{for one value of a}\\(D)\;\text{for no values of a} \end{array}$

$3a+a^2-2=0$
$a^2+3a-2=0$
=> $a=\large \frac{-3 \pm \sqrt {9+8}}{2}$
$\qquad = \large\frac{-3\pm \sqrt {17}}{2}$