Multiple choice

Solve the following quadratic equations and choose the correct answer accordingly. I. x2 - 11x + 30 = 0 II. y2 - 15y + 54 = 0

  1. x > y

  2. x < y

  3. x ≤ y

  4. x ≥ y

  5. x = y or No relation can be established.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

I: x^2 - 11x + 30 = 0 => (x-5)(x-6) = 0 => x = 5, 6. II: y^2 - 15y + 54 = 0 => (y-6)(y-9) = 0 => y = 6, 9. Comparing: 5 < 6, 5 < 9, 6 = 6, 6 < 9. Thus, x <= y.

AI explanation

Using the factorization method for quadratic equations, the first equation x2 - 11x + 30 = 0 yields factors (x - 5) and (x - 6), giving roots x = 5 and x = 6. The second equation y2 - 15y + 54 = 0 yields factors (y - 6) and (y - 9), giving roots y = 6 and y = 9. Comparing the values, we find x = 5 is less than both y values, while x = 6 is equal to one y value and less than the other, establishing the overall relation x is less than or equal to y.

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