# For what values of k, the equation

Question:

For what values of $k$, the equation $k x^{2}-6 x-2=0$ has real roots?

(a) $k \leq \frac{-9}{2}$

(b) $k \geq \frac{-9}{2}$

(c) $k \leq-2$

(d) None of these

Solution:

(b) $k \geq \frac{-9}{2}$

It is given that the roots of the equation $\left(k x^{2}-6 x-2=0\right)$ are real.

$\therefore D \geq 0$

$\Rightarrow\left(b^{2}-4 a c\right) \geq 0$

$\Rightarrow(-6)^{2}-4 \times k \times(-2) \geq 0$

$\Rightarrow 36+8 k \geq 0$

$\Rightarrow k \geq \frac{-36}{8}$

$\Rightarrow k \geq \frac{-9}{2}$