Multiple choice

Directions: Choose your answer as: One root of x2 - 9x + k = 0 is twice the other. Quantity A Quantity B K 27

  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.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For x^2 - 9x + k = 0, let the roots be r and 2r. Sum of roots: 3r = 9, so r = 3. Product of roots: (r)(2r) = 2r^2 = k. Thus, k = 2(3^2) = 18. Since 18 < 27, Quantity B is greater.

AI explanation

Let the roots be a and two a; their sum equals nine, so three a equals nine and a equals three. This makes the roots three and six, and their product gives k equals eighteen. Therefore, since twenty seven is greater than eighteen, quantity B is greater than quantity A.

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