For what positive values of $k$, does the quadratic equation $3 x^2-k x+3=0$ not have real roots?

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Oct 18
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**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.

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