Multiple choice

Directions: In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer. I. 25x2 – 90x + 72 = 0II. y2 + 26y + 168 = 0

  1. x > y

  2. x ≤ y

  3. x ≥ y

  4. x < y

  5. x = y or relationship between x and y can't be established
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A Correct answer
Explanation

Eq I: 25x^2 - 90x + 72 = 0. Roots: x = [90 +/- sqrt(8100 - 7200)] / 50 = (90 +/- 30) / 50. x = 1.2 or 2.4. Eq II: y^2 + 26y + 168 = 0. Roots: y = [-26 +/- sqrt(676 - 672)] / 2 = (-26 +/- 2) / 2. y = -12 or -14. Since 1.2 and 2.4 are both greater than -12 and -14, x > y.

AI explanation

Factoring the first quadratic equation 25x2 - 90x + 72 = 0 gives (5x - 6)(5x - 12) = 0, yielding roots x = 6/5 and x = 12/5. Factoring the second equation y2 + 26y + 168 = 0 gives (y + 12)(y + 14) = 0, yielding negative roots y = -12 and y = -14. Since both values of x are positive and both values of y are negative, x is always greater than y.

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