Multiple choice

The value of $k$ for which $3$ is a root of the equation $\displaystyle kx^{2}-7x+3=0$ is

  1. $2$
  2. $-2$
  3. $3$
  4. $-3$
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A Correct answer
Explanation

If 3 is a root, it must satisfy the equation: k(3)^2 - 7(3) + 3 = 0. This gives 9k - 21 + 3 = 0, so 9k = 18, which means k = 2.

AI explanation

Since 3 is a root of the equation, it must satisfy the equation, so we substitute x = 3 into k(3)^2 - 7(3) + 3 = 0. This simplifies to 9k - 21 + 3 = 0, which further reduces to 9k - 18 = 0. Solving for k gives 9k = 18, resulting in k = 2.

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