Multiple choice

Directions: Compare the two quantities in A and B. The roots of the equation x2 - kx + 14 = 0 are imaginary. Quantity A Quantity B Greatest value of k 6.8

  1. Quantity A is greater than quantity B.

  2. Quantity B is greater than quantity A.

  3. Both quantities are equal.

  4. The relationship between the quantities cannot be determined.
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A Correct answer
AI explanation

For the quadratic equation x^2 - kx + 14 = 0 to have imaginary roots, the discriminant must be strictly less than zero, establishing the inequality k^2 - 56 < 0. Solving this inequality gives the range of k as being between the negative and positive square roots of 56, which are approximately -7.48 and 7.48. The greatest possible value for k within this continuous interval is just under 7.48. Since 7.48 is greater than the given value of 6.8, Quantity A is greater than quantity B.

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