Multiple choice

For a quadratic polynomial $p\left(x\right) = kx^2 - 2x - 3k$, if sum of zeroes are equal to the product of zeroes, then the value of $k$ is

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

For a quadratic equation ax^2 + bx + c = 0, the sum of zeroes is -b/a and the product is c/a. Here, -(-2)/k = -3k/k, which simplifies to 2/k = -3. Thus, k = -2/3.

AI explanation

For the polynomial p(x) = kx^2 - 2x - 3k, Vieta's formulas state that the sum of the zeroes is 2/k and the product is -3k/k = -3. Equating the sum and product gives 2/k = -3. Solving this yields k = -2/3.

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