Multiple choice

If $r = 3$ is a root of quadratic equation $kr^{2} - kr - 3 = 0$, then value of $k$ is :

  1. $\dfrac{1}{2}$
  2. $2$
  3. $-2$
  4. $-\dfrac{1}{2}$
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A Correct answer
Explanation

Substitute r = 3 into the equation: k(3^2) - k(3) - 3 = 0. This simplifies to 9k - 3k - 3 = 0, or 6k = 3, which gives k = 1/2.

AI explanation

Since r = 3 is a root of the quadratic equation, substituting r = 3 into the equation kr^2 - kr - 3 = 0 gives k(3)^2 - k(3) - 3 = 0. Simplifying this results in 9k - 3k - 3 = 0, which further reduces to 6k = 3. Solving for k gives k = 1/2.

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