For what value of k, the equation $k x^{2} - 6 x - 2 = 0$ has equal roots.

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\frac{- 9}{2}

\frac{9}{2}

\frac{- 9}{4}

\frac{9}{4}

answer is A.

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Detailed Solution

Concept- We will use the fact that the discriminant value for equal roots is zero to determine the value of k.
In order to solve the above quadratic equation, we must first identify its discriminant, which can be done as follows.

D = b^{2} - 4 ac

D = {(- 6)}^{2} - 4 k (- 2)

D = 36 + 8 k

To ensure that the equation's roots are equal, we must now set D=0. As a result, we obtain

D = 0 = 36 + 8 k

k = \frac{- 36}{8}

k = \frac{- 9}{2}

So, the required value is

\frac{- 9}{2}

Hence, the correct answer is option 1)

\frac{- 9}{2}

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