Multiple choice

In the following questions two equations numbered I and II are given. You have to solve both the equations and choose the correct option. I. x2 +15x +54 = 0 II. y2-5y -66 = 0

  1. x < y

  2. x > y

  3. x ≤ y

  4. x ≥ y

  5. x = y or relationship cannot be established.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

I: x^2 + 15x + 54 = 0 => (x+6)(x+9) = 0 => x = -6, -9. II: y^2 - 5y - 66 = 0 => (y-11)(y+6) = 0 => y = 11, -6. Comparing: -6 <= 11, -6 <= -6, -9 <= 11, -9 <= -6. Thus, x <= y.

AI explanation

Factoring equation one gives (x + 9)(x + 6) = 0, meaning x = -9 or x = -6. Factoring equation two gives (y - 11)(y + 6) = 0, meaning y = 11 or y = -6. Both x values are less than 11, and while x can equal y at -6, it is never greater than y; therefore, x is less than or equal to y.

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