Multiple choice

In each of the following questions two equations are given. Solve these equations and give answer: (a) if π‘₯ β‰₯ 𝑦, i.e., π‘₯ is greater than or equal to 𝑦 (b) if π‘₯ > 𝑦, i.e., π‘₯ is greater than 𝑦 (c) if π‘₯ ≀ 𝑦, i.e., π‘₯ is less than or equal to 𝑦 (d) if π‘₯ < 𝑦, i.e., π‘₯ is less than 𝑦 (e) π‘₯ = 𝑦 or no relation can be established between π‘₯ and y I. xΒ² βˆ’ 12 x + 35 = 0 II. yΒ² βˆ’ 11 y + 24 = 0

  1. e

  2. b

  3. c

  4. d

  5. a
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

I: x^2 - 12x + 35 = 0 -> (x-7)(x-5) = 0, so x = 5, 7. II: y^2 - 11y + 24 = 0 -> (y-8)(y-3) = 0, so y = 3, 8. Comparing the sets {5, 7} and {3, 8}: 5 > 3, 5 < 8, 7 > 3, 7 < 8. Since x can be both greater than and less than y, no relation can be established.

AI explanation

Factorizing the first equation x^2 - 12x + 35 = 0 gives the roots x = 5 and x = 7. Factorizing the second equation y^2 - 11y + 24 = 0 gives the roots y = 3 and y = 8. When comparing x = 5 and x = 7 against y = 3 and y = 8, x is greater than one y value but less than the other, so no relation can be established between x and y.

Keep practicing β€” related questions