Multiple choice

Directions: In this question, two equations numbered I and II are given. You have to solve both the equations and mark the correct answer. I. 3x2 - 19x + 30 = 0 II. 5y2 - 29y + 42 = 0

  1. if x > y

  2. if x < y

  3. if x ≤ y

  4. if x ≥ y

  5. if x = y or no relationship can be established between 'x' and 'y'
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Solving I: 3x^2 - 19x + 30 = 0 gives (3x - 10)(x - 3) = 0, so x = 3.33 or 3. Solving II: 5y^2 - 29y + 42 = 0 gives (5y - 14)(y - 3) = 0, so y = 2.8 or 3. Comparing values: x can be 3.33 or 3, y can be 2.8 or 3. Since 3.33 > 2.8, 3.33 > 3, 3 > 2.8, and 3 = 3, x is always >= y.

AI explanation

Factoring the first equation, 3x2 minus 19x plus 30 equals zero, gives (3x minus 10)(x minus 3) equals zero, resulting in x equals 10 divided by 3 (approximately 3.33) or x equals 3. Factoring the second equation, 5y2 minus 29y plus 42 equals zero, gives (5y minus 14)(y minus 3) equals zero, resulting in y equals 14 divided by 5 (2.8) or y equals 3. Comparing the values, the smallest root of x is greater than the smallest root of y, and the remaining roots are equal to each other. Hence, x is greater than or equal to y.

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