Multiple choice

Directions: In the following question, two equations are given. You have to solve both the equations and choose the correct relationship accordingly. I. 9x2 - 31x + 26 =0 II. 5y2 - 12y + 7 = 0

  1. x > y

  2. x ≥ y

  3. x < y

  4. x ≤ y

  5. x = y, or no relationship can be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Solving 9x^2 - 31x + 26 = 0: roots are 2 and 13/9 (approx 1.44). Solving 5y^2 - 12y + 7 = 0: roots are 1 and 1.4. Since 2 > 1.4 and 1.44 > 1.4, x is generally greater than y.

AI explanation

Factor the first quadratic equation by splitting the middle term to get (x - 2)(9x - 13) = 0, yielding the roots x = 2 and x = 13/9. For the second equation, factoring gives (y - 1)(5y - 7) = 0, which provides the roots y = 1 and y = 7/5. Since both roots of x are greater than both roots of y, the relationship is x > y.

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