Multiple choice

Directions: In the following question, two equations numbered I and II are given. You have to solve both the equations and give the answer. (I) 2d2 - 7d + 6 = 0 (II) 5e2 - 9e + 4 = 0

  1. d > e

  2. d ≤ e

  3. d < e

  4. d ≥ e

  5. d = e, or no relation between d and e
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Solving 2d^2 - 7d + 6 = 0: (2d-3)(d-2) = 0, so d = 1.5, 2. Solving 5e^2 - 9e + 4 = 0: (5e-4)(e-1) = 0, so e = 0.8, 1. Comparing: 1.5 > 0.8, 1.5 > 1, 2 > 0.8, 2 > 1. Thus, d > e.

AI explanation

Solving the first equation, 2d squared minus 7d plus 6 equals 0, by splitting the middle term gives 2d squared minus 3d minus 4d plus 6 equals 0. Factoring by grouping yields d times the quantity of 2d minus 3 minus 2 times the quantity of 2d minus 3 equals 0, resulting in roots d equals 2 and d equals 1.5. Solving the second equation, 5e squared minus 9e plus 4 equals 0, by splitting the middle term gives 5e squared minus 5e minus 4e plus 4 equals 0. Factoring by grouping yields e times the quantity of 5e minus 5 minus 4 times the quantity of e minus 1 equals 0, resulting in roots e equals 1 and e equals 0.8. Comparing both sets of roots shows that both values of d are strictly greater than both values of e, so d > e.

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