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. 8x2 + 20x + 12 = 0 II. 4y2 + 39y + 56 = 0

  1. x > y

  2. x < y

  3. x = y or no relation can be established

  4. x ≥ y

  5. x ≤ y
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A Correct answer
Explanation

Equation I: 8x^2 + 20x + 12 = 0 -> 2x^2 + 5x + 3 = 0 -> (2x+3)(x+1) = 0. Roots are x = -1.5, -1. Equation II: 4y^2 + 39y + 56 = 0 -> (4y+7)(y+8) = 0. Roots are y = -1.75, -8. Comparing roots, -1 > -1.75 and -1 > -8, and -1.5 > -1.75 and -1.5 > -8. Thus, x > y.

AI explanation

Using the method of factorization on the first equation, we split 8x2 + 20x + 12 = 0 into (2x + 2) and (4x + 6) = 0, which yields the roots x = -1 or -3/2. The second equation factors into (4y + 7) and (y + 8) = 0, yielding the roots y = -7/4 or -8. Since -1 is greater than both -7/4 and -8, and -3/2 is also greater than both -7/4 and -8, the relationship is x > y.

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