Multiple choice

If one root of the quadratic equation $kx^{2}\,-\,7x\,+\,12\,=\,0$ is 3, then find the value of $k$.

  1. 4

  2. 3

  3. 2

  4. 1
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D Correct answer
Explanation

If 3 is a root, then k(3)^2 - 7(3) + 12 = 0. This simplifies to 9k - 21 + 12 = 0, so 9k = 9, and k = 1.

AI explanation

Substitute the given root x equals 3 into the quadratic equation k times x squared minus 7x plus 12 equals 0. This results in k times 3 squared minus 7 times 3 plus 12 equals 0. Simplifying the terms gives 9k minus 21 plus 12 equals 0, which further reduces to 9k minus 9 equals 0. Solving this yields 9k equals 9, so k equals 1.

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