Multiple choice

Directions: In this question, two equations (i) and (ii) are given, you have to solve both the equations and give answer accordingly. (i) 4x2 – 12x + 9 = 0 (ii) 16y2 – 24y + 5 = 0

  1. x ≥ y

  2. x < y

  3. x ≤ y

  4. x > y

  5. x = y or no relation can be established between x & y.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Solving 4x^2 - 12x + 9 = 0 gives (2x - 3)^2 = 0, so x = 1.5. Solving 16y^2 - 24y + 5 = 0 using the quadratic formula gives y = (24 +/- sqrt(576 - 320))/32 = (24 +/- 16)/32, resulting in y = 1.25 or y = 0.25. Since 1.5 > 1.25 and 1.5 > 0.25, x > y.

AI explanation

Equation I is a perfect square, giving (2x minus 3) squared = 0 and x = 3/2. Factoring equation II gives (4y minus 1)(4y minus 5) = 0, so y = 1/4 or y = 5/4. Since 3/2 is greater than both 1/4 and 5/4, x > y.

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