Multiple choice

Directions: The following question consists of two equations. You are required to solve the equations and identify the correct answer from the alternatives given below. I. x2 – 20x + 75 = 0 II. 4y2 – 32y + 60 = 0

  1. x > y

  2. x ≥ y

  3. x ≤ y

  4. x < y

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

I: x^2 - 20x + 75 = 0 => (x-15)(x-5) = 0 => x = 5, 15. II: 4y^2 - 32y + 60 = 0 => y^2 - 8y + 15 = 0 => (y-5)(y-3) = 0 => y = 3, 5. Comparing values: x can be 5 or 15, y can be 3 or 5. In all cases, x >= y.

AI explanation

Factoring equation I gives (x - 15)(x - 5) = 0, so the roots are x = 5 and x = 15. Dividing equation II by 4 gives y^2 - 8y + 15 = 0, which factors into (y - 5)(y - 3) = 0, yielding y = 3 and y = 5. Comparing these roots, 5 is greater than 3 and equal to 5, while 15 is greater than both 3 and 5, meaning x is greater than or equal to y.

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