Multiple choice

If one root of the equation $x^2-4x+k=0$ is $6$, then the value of k will be

  1. $12$
  2. $2$
  3. $-2$
  4. $-12$
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D Correct answer
Explanation

If 6 is a root, it must satisfy the equation: 6^2 - 4(6) + k = 0. 36 - 24 + k = 0. 12 + k = 0, so k = -12.

AI explanation

Since x = 6 is a root of the quadratic equation x^2 - 4x + k = 0, it must satisfy the equation. Substituting 6 for x gives 6^2 - 4(6) + k = 0. Simplifying this yields 36 - 24 + k = 0, so 12 + k = 0. Solving for k gives k = -12.

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