Multiple choice

If one root of the equation $3x^2+kx-81=0$ is the square of the other, find $k$.

  1. $k= -18$
  2. $k= 18$
  3. $k= -8$

  4. None of these
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A Correct answer
Explanation

Let roots be r and r^2. Product r^3 = -81/3 = -27, so r = -3. Sum r + r^2 = -k/3. (-3) + (-3)^2 = -3 + 9 = 6. So -k/3 = 6, k = -18.

AI explanation

Let the roots be p and p^2. Using the product of roots formula, (p)(p^2) = -81/3, so p^3 = -27 and p = -3. The roots are -3 and 9. Using the sum of roots formula, -k/3 equals -3 + 9, which gives -k/3 = 6, yielding k = -18. The result is k = -18.

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