Multiple choice

In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer. I. x2 – 0.5x – 39 = 0 II. y2 – 15.5y + 60 = 0

  1. if x > y

  2. if x ≤ y

  3. if x ≥ y

  4. if x < y

  5. if x = y or relationship between x and y can't be established
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

I: x^2 - 0.5x - 39 = 0. Roots using quadratic formula: (0.5 +/- sqrt(0.25 + 156)) / 2 = (0.5 +/- 12.5) / 2. x = 6.5 or -6. II: y^2 - 15.5y + 60 = 0. Roots: (15.5 +/- sqrt(240.25 - 240)) / 2 = (15.5 +/- 0.5) / 2. y = 8 or 7.5. Comparing x and y, x < y.

AI explanation

Using the quadratic formula for the first equation x2 - 0.5x - 39 = 0, we get x = 6.5 or x = -6. For the second equation y2 - 15.5y + 60 = 0, the roots are y = 6 and y = 9.5. Comparing the roots, -6 is less than both 6 and 9.5, and 6.5 is also less than both 6 and 9.5. Therefore, x is always less than y.

Keep practicing — related questions