Multiple choice

Directions: In the following question, equations numbered I and II are given. You have to solve both the equations and mark the correct option. I. x2 - 15x + 56 = 0 II. y2 - 23y + 132 = 0

  1. x < y

  2. x ≤ y

  3. x > y

  4. x ≥ y

  5. x = y or the relationship cannot be determined
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Solving x^2 - 15x + 56 = 0 gives (x-7)(x-8)=0, so x is 7 or 8. Solving y^2 - 23y + 132 = 0 gives (y-11)(y-12)=0, so y is 11 or 12. Since all values of x are less than all values of y, x < y.

AI explanation

Factoring the first equation, x2 minus 15x plus 56 equals zero, yields (x minus 7)(x minus 8) equals zero, which gives the roots x equals 7 and x equals 8. Factoring the second equation, y2 minus 23y plus 132 equals zero, yields (y minus 11)(y minus 12) equals zero, which gives the roots y equals 11 and y equals 12. Since the largest possible value of x is 8 and the smallest possible value of y is 11, every value of x is strictly smaller than every value of y. Therefore, x is less than y.

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