Find the values of $k$ for which the quadratic equation $k x(x - 2) + 6 = 0$ has two equal roots.
Step-by-Step Solution
Key Concept: $k x^2 - 2k x + 6 = 0$. Equal roots $\Rightarrow D = 4k^2 - 24k = 0 \Rightarrow 4k(k - 6) = 0 \Rightarrow k = 6$ (since $k <br>eq 0$).
$k x^2 - 2k x + 6 = 0$. $D = (-2k)^2 - 4(k)(6) = 4k^2 - 24k = 0$. [1.0 Mark]
$4k(k - 6) = 0$. Since $k
eq 0$ for a quadratic equation, $k = 6$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Setting $D = 4k^2 - 24k = 0$: 1.0 Mark
Solving $k = 6$: 1.0 Mark
Correct Answer: