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. 3x2 – 4x + 1 = 0 II. y2 – 4y + 3 = 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
C Correct answer
Explanation

Equation I: 3x^2 - 4x + 1 = 0 -> (3x-1)(x-1) = 0 -> x = 1/3, 1. Equation II: y^2 - 4y + 3 = 0 -> (y-3)(y-1) = 0 -> y = 1, 3. Comparing values: x=1/3 <= y=1, x=1/3 <= y=3, x=1 <= y=1, x=1 <= y=3. Thus x <= y.

AI explanation

Factoring equation I gives (3x - 1)(x - 1) = 0, yielding roots x = 1/3 and x = 1. Factoring equation II gives (y - 1)(y - 3) = 0, yielding roots y = 1 and y = 3. Comparing the values, 1/3 is less than both 1 and 3, and 1 is equal to 1 but less than 3, meaning x is less than or equal to y.

Keep practicing — related questions