Multiple choice

Directions: In the following question, equations numbered I and II are given. You have to solve both the equations and mark the correct option. I. x2 + 13x + 42 = 0 II. y2 + 19y + 90 = 0

  1. x < y

  2. x ≤ y

  3. x > y

  4. x ≥ y

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

Equation I: x^2 + 13x + 42 = 0 => (x+6)(x+7) = 0 => x = -6, -7. Equation II: y^2 + 19y + 90 = 0 => (y+9)(y+10) = 0 => y = -9, -10. Comparing values: -6 > -9, -6 > -10, -7 > -9, -7 > -10. Thus, x > y.

AI explanation

Using the method of factorization, the first equation becomes (x + 6)(x + 7) = 0, so x is either -6 or -7. The second equation factors to (y + 9)(y + 10) = 0, meaning y is either -9 or -10. Since -6 and -7 are both greater than -9 and -10 on the number line, it follows that x > y.

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