Multiple choice

In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer I. 2x²+28=15x II. -17y+36=-2y²

  1. if x < y

  2. if x ≤ y

  3. if x = y or no relation can established

  4. if x > y be

  5. if x ≥ y
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

I: 2x^2 - 15x + 28 = 0. Roots: (2x-7)(x-4) = 0, so x = 3.5, 4. II: 2y^2 - 17y + 36 = 0. Roots: (2y-9)(y-4) = 0, so y = 4.5, 4. Comparing: x=3.5 < y=4.5, x=3.5 < y=4, x=4 <= y=4.5, x=4 = y=4. Thus x <= y.

AI explanation

Rearranging equation I gives 2x squared minus 15x plus 28 equals 0, which factors to (2x - 7)(x - 4) = 0, yielding x = 3.5 and x = 4. Rearranging equation II gives 2y squared minus 17y plus 36 equals 0, which factors to (2y - 9)(y - 4) = 0, yielding y = 4.5 and y = 4. Comparing the values, x is less than or equal to y because the maximum value of x is 4, which equals the smaller y value, and 3.5 is less than 4. Therefore, x is less than or equal to y.

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