Multiple choice

Directions: In the following question, two equations numbered (I) and (II) are given. Student should solve both the equations and mark appropriate answer. I. 9x2 - 18x + 8 = 0 II. 7y2 - 17y + 6 = 0

  1. If x > y

  2. If x = y or no relation can be established

  3. If x < y

  4. If x ≥ y

  5. If x ≤ y
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Solve 9x^2 - 18x + 8 = 0: x = (18 +/- sqrt(324 - 288))/18 = (18 +/- 6)/18. x = 4/3 or 2/3. Solve 7y^2 - 17y + 6 = 0: y = (17 +/- sqrt(289 - 168))/14 = (17 +/- 11)/14. y = 2 or 3/7. Comparing values, no consistent relation exists.

AI explanation

Factor the first equation 9x squared minus 18x plus 8 equals 0 to find the roots are x equals 4/3 and x equals 2/3. Factor the second equation 7y squared minus 17y plus 6 equals 0 to find the roots are y equals 2 and y equals 3/7. Comparing the values, 2/3 is less than 2 but greater than 3/7, while 4/3 is less than 2 but greater than 3/7. Since no single inequality holds for all possible pairs of roots, no relation can be established.

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