Multiple choice

Directions: Solve the given equations and identify the correct answer. x2 + 10x + 25 = 0 6y2 - 19y + 10 = 0

  1. x > y

  2. x ≥ y

  3. x < y

  4. x ≤ y

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

x^2 + 10x + 25 = 0 -> (x+5)^2 = 0 -> x = -5. 6y^2 - 19y + 10 = 0 -> 6y^2 - 15y - 4y + 10 = 0 -> 3y(2y-5) - 2(2y-5) = 0 -> (3y-2)(2y-5) = 0 -> y = 2/3 or 5/2. Since -5 < 2/3 and -5 < 5/2, x < y.

AI explanation

The first equation x^2 + 10x + 25 = 0 is a perfect square, which factors to (x + 5)^2 = 0, giving the single root x = -5. For the second equation 6y^2 - 19y + 10 = 0, factoring yields (2y - 5)(3y - 2) = 0, giving the roots y = 5/2 and y = 2/3. Comparing the values, x = -5 is strictly less than both positive values of y. Therefore, the relationship x < y holds true.

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