SOLUTION —
GIVEN : Quadratic equation $3 x^2-k x+3=0$, has no real roots.
On comparing the given equation with $a x^2+b x+c=0$, we have :
$a=3, b=-k, c=3 \text {. }$
Then, discriminant,
$\begin{aligned}\mathrm{D} & =b^2-4 a c \\& =(-k)^2-4 \times 3 \times 3 \\& =k^2-36\end{aligned}$
But for no real roots, $\mathrm{D}<0$
Then, $k^2-36<0$
$\begin{array}{ll}\Rightarrow & k^2<36 \\\Rightarrow & k< \pm 6 \\\Rightarrow & k>-6 \text { or } k<6\end{array}$
Hence, The value of $k<6$ (positive value) for no real roots.