Multiple choice

\text{What values of K if the roots of the equation } x^2 + 2(K-4)x + 2K = 0 \text{ are equal?}

  1. 6, 2

  2. 7, 2

  3. 8, 2

  4. 3, 2
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C Correct answer
Explanation

Equal roots when discriminant = 0. For ax² + bx + c: D = b² - 4ac. Here: a=1, b=2(K-4), c=2K. D = 4(K-4)² - 8K = 0 → 4(K² - 8K + 16) - 8K = 0 → 4K² - 32K + 64 - 8K = 0 → 4K² - 40K + 64 = 0 → K² - 10K + 16 = 0 → (K-8)(K-2) = 0 → K = 8, 2.

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