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NDA 2026 · PYQ · Quadratic Equations · easy

For a given k, what is the minimum value of x² + kx + k²?

Answer

The correct answer is C: 3k²/4. Completing the square: x² + kx + k² = (x + k/2)² + k² - k²/4 = (x + k/2)² + 3k²/4. Minimum value is 3k²/4 when x = -k/2.

  1. A.0
  2. B.k²/4
  3. C.3k²/4✓ Correct
  4. D.k²/2

Explanation

Completing the square: x² + kx + k² = (x + k/2)² + k² - k²/4 = (x + k/2)² + 3k²/4. Minimum value is 3k²/4 when x = -k/2.
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