Multiple choice

I. 5x² - 36 = 12² II. y² + 17y + 72 = 0 Solve the given quadratic equations and mark the correct option based on your answer— (a) x > y (b) x ≥ y (c) x < y (d) x ≤ y (e) x = y or no relation can be established between x and y.

  1. A

  2. B

  3. C

  4. D

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

I: 5x^2 - 36 = 144 => 5x^2 = 180 => x^2 = 36 => x = 6, -6. II: y^2 + 17y + 72 = 0 => (y+8)(y+9) = 0 => y = -8, -9. Comparing x and y, 6 > -8, 6 > -9, -6 > -8, -6 > -9. Thus x > y.

AI explanation

Solving the first equation gives 5x squared = 144, so x equals 12 over the square root of 5 or negative 12 over the square root of 5, which approximately equals 5.36 and negative 5.36. Factoring the second equation using the sum and product method gives y plus 8 and y plus 9, so y equals negative 8 or negative 9. Comparing both positive and negative values of x with both values of y shows that x is always greater than y.

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