Multiple choice

Directions: In this question, two equations numbered I and II are given. You have to solve both the equations and mark the correct answer. I. 6x2 + 11x - 112 = 0 II. 2y2 - 15y + 28 = 0

  1. if x < y

  2. if x > y

  3. if x ≤ y

  4. if x ≥ y

  5. if x = y or no relationship can be established between 'x' and 'y'
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

I: 6x^2 + 11x - 112 = 0. Roots are x = 3.5, -5.33. II: 2y^2 - 15y + 28 = 0. Roots are y = 4, 3.5. Comparing: 3.5 <= 4 and 3.5 <= 3.5, -5.33 <= 4 and -5.33 <= 3.5. Thus, x <= y.

AI explanation

Using the method of factorization, the first quadratic equation splits into the factors (2x - 7) and (3x + 16) = 0, which yields the roots x = 7/2 or -16/3. The second equation factors into (y - 6) and (2y - 7) = 0, yielding the roots y = 6 or 7/2. When comparing these values, the value of -16/3 is less than both 6 and 7/2, and the value of 7/2 equals the smaller root of y but is less than 6, establishing that x is always less than or equal to y.

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