Multiple choice

Derive the relationship between x and y by solving the given equations: x2 + 27x + 50 = 0 2y2 - 21y + 55 = 0

  1. x < y

  2. x > y

  3. x ≥ y

  4. x ≤ y

  5. x = y or relationship can not be established.
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A Correct answer
Explanation

x^2 + 27x + 50 = 0 => (x + 25)(x + 2) = 0, so x = -25 or -2. 2y^2 - 21y + 55 = 0 => (2y - 11)(y - 5) = 0, so y = 5.5 or 5. In all cases, x < y.

AI explanation

Factoring the first equation x squared plus 27x plus 50 equals 0 gives (x + 25)(x + 2) equals 0, so x is -25 or -2. Factoring the second equation 2y squared minus 21y plus 55 equals 0 gives (2y - 11)(y - 5) equals 0, so y is 5.5 or 5. Both roots of x are negative while both roots of y are positive, so x is strictly less than y.

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