Multiple choice

Directions: In this question, two equations (I) and (II) are given. You have to solve both the equations and give answer I. 25x2 - 30x - 27 = 0 II. 25y2 + 60y + 27 = 0

  1. x > y

  2. x ≥ y

  3. x < y

  4. x ≤ y

  5. x = y or the relationship between x and y cannot be established
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Solving 25x^2 - 30x - 27 = 0 gives roots x = 1.8 and x = -0.6. Solving 25y^2 + 60y + 27 = 0 gives roots y = -0.6 and y = -1.8. Comparing the sets, x >= y holds true for all combinations.

AI explanation

For the first equation, 25x2 minus 30x minus 27 equals zero, the quadratic formula gives x equals (30 plus or minus 900 plus 2700 divided by 50), simplifying to x equals 3 or x equals minus 0.6. For the second equation, 25y2 plus 60y plus 27 equals zero, factoring yields (5y plus 3)(5y plus 9) equals zero, giving y equals minus 0.6 or y equals minus 1.8. Since both possible values of x are greater than or equal to both possible values of y, the relationship is that x is greater than or equal to y.

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