Multiple choice

If one of the zeroes of the quadratic polynomial $(k-1)x^{2}+kx+1$ is $-3$, then the value of $k$ is.

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

Substitute x = -3 into the polynomial (k-1)x^2 + kx + 1 = 0. This gives (k-1)(9) - 3k + 1 = 0, which simplifies to 9k - 9 - 3k + 1 = 0, or 6k = 8, so k = 4/3.

AI explanation

Since -3 is a zero of the quadratic polynomial (k-1)x^2 + kx + 1, substitute x = -3 into the equation. This gives (k - 1)(-3)^2 + k(-3) + 1 = 0, which simplifies to 9k - 9 - 3k + 1 = 0. Combining the terms results in 6k - 8 = 0. Solving this linear equation yields k = 8/6, which simplifies to 4/3.

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