Multiple choice

Directions: In the question, two equations numbered (I) and (II) are given. You have to solve both the equations and then mark the appropriate answer. (I) 8x2 – 144x + 648 = 0 (II) y2 – 5y – 36 = 0

  1. x = y or no relationship can be established between them.

  2. x > y

  3. x < y

  4. x ≥ y

  5. x ≤ y
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Eq I: 8x^2 - 144x + 648 = 0 -> x^2 - 18x + 81 = 0 -> (x-9)^2 = 0 -> x = 9. Eq II: y^2 - 5y - 36 = 0 -> (y-9)(y+4) = 0 -> y = 9, -4. Comparing x=9 with y=9 or -4, x >= y.

AI explanation

Dividing equation I by 8 gives x squared minus 18x + 81 = 0, which factors into (x minus 9) squared = 0 to yield x = 9. Factoring equation II gives (y minus 9)(y + 4) = 0, so y = 9 or y = negative 4. Since 9 is greater than or equal to both values of y, x is greater than or equal to y.

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