Multiple choice

Directions: In the question, two equations numbered I and II are given. You have to find the relationship between them by solving both the equations and then mark the answer accordingly. I. 12x2 - 16x + 4 = 0 II. 60y2 - 60y + 15 = 0

  1. x > y

  2. x < y

  3. x = y or no relation can be established

  4. x ≥ y

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

Equation I: 12x^2 - 16x + 4 = 0 simplifies to 3x^2 - 4x + 1 = 0, which factors to (3x-1)(x-1)=0, giving x = 1/3 or 1. Equation II: 60y^2 - 60y + 15 = 0 simplifies to 4y^2 - 4y + 1 = 0, which is (2y-1)^2 = 0, giving y = 1/2. Comparing the roots, x=1 > y=1/2 and x=1/3 < y=1/2, so no consistent relationship exists.

AI explanation

By dividing equation one by four, we get three times x squared minus four x plus one equals zero, which factors into (3x minus one) times (x minus one) giving x values of 1/3 and 1. Dividing equation two by five yields twelve times y squared minus twelve y plus three equals zero, and dividing further by three gives four times y squared minus four y plus one equals zero, which is a perfect square (2y minus one) squared giving y equal to 1/2. Since 1/3 is less than 1/2 but 1 is greater than 1/2, x equals y or no relation can be established.

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