Multiple choice

The value of k for which the equations x2 + kx + 64 = 0 and x2 - 8x + k = 0 will have both real roots is

  1. 8

  2. 16

  3. – 64

  4. 32

  5. – 56
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B Correct answer
AI explanation

For both quadratic equations to have real roots, their discriminants must be greater than or equal to zero. For the first equation, b^2 - 4ac >= 0 means k^2 - 256 >= 0, so k >= 16 or k <= -16. For the second equation, (-8)^2 - 4k >= 0, which simplifies to 64 - 4k >= 0, giving k <= 16. The only value among the choices that satisfies both conditions is 16, where k = 16 meets the equality limits of both discriminants.

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