Multiple choice

One root of the equation $x^2 + kx -8 = 0$ is the square of the other. What is the value of k

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

Let the roots be r and r^2. By Vieta's formulas, r + r^2 = -k and r * r^2 = -8. Thus, r^3 = -8, which gives r = -2. Substituting r = -2 into the sum equation, -2 + (-2)^2 = -k, so -2 + 4 = -k, which means k = -2.

AI explanation

If one root is r and the other is r^2, their product gives r^3 = -8, meaning r = -2. The two roots are then -2 and 4, and their sum is 2. For a quadratic equation x^2 + kx - 8 = 0, the sum of the roots equals -k. Setting -k = 2 gives the value of k as -2.

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