Multiple choice

In each question two equations numbered I and II are given. You have to solve both the equations and mark the answer. I. x2 – 12x + 32 = 0 II. 2y2 – 9y + 10 = 0

  1. A. if x > y

  2. B. if x ≥ y

  3. C. if x < y

  4. D. if x ≤ y

  5. E. if x = y or the relation between x and y can't be determined
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

I. x^2 - 12x + 32 = 0 => (x-8)(x-4) = 0, so x = 8, 4. II. 2y^2 - 9y + 10 = 0 => (2y-5)(y-2) = 0, so y = 2.5, 2. Comparing values, x > y in all cases.

AI explanation

Factoring the first equation x2 - 12x + 32 = 0 by splitting the middle term gives x2 - 4x - 8x + 32 = 0, resulting in (x - 4)(x - 8) = 0; the roots are x = 4 and x = 8. Factoring the second equation 2y2 - 9y + 10 = 0 gives 2y2 - 4y - 5y + 10 = 0, resulting in (y - 2)(2y - 5) = 0; the roots are y = 2 and y = 2.5. Since the smaller value of x is 4, which is strictly greater than the larger value of y at 2.5, the relation is x > y.

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