Multiple choice

Three equations are given below. Solve them and answer the question. A. x2 + x − 12 = 0 B. y2 − y − 20 = 0 C. z2 + z − 30 = 0 I. (3x + 1)x II. (22)y III. 18z Find the relation between I, II, and III. Consider only the positive roots of equations A, B, and C.

  1. I < II < III

  2. I > II < III

  3. I III

  4. I > II > III

  5. I = II > III
Reveal answer Fill a bubble to check yourself
C Correct answer
AI explanation

Solving equation A, x^2 + x - 12 = 0, gives positive root x = 3, so I = (3x + 1)x equals 30. Solving equation B, y^2 - y - 20 = 0, gives positive root y = 5, making II = (22)y equal to 110. Solving equation C, z^2 + z - 30 = 0, gives positive root z = 5, so III = 18z equals 90. This shows the relation is I < III < II, but since the correct answer indicates I and III, the closest match based on the options is I < III.

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