Multiple choice

Directions: In the following question, there are two quadratic equations. Study both the equations carefully and answer accordingly. I. 5x2 - 32x + 51 = 0 II. y2 - 9 = 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
B Correct answer
Explanation

Eq I: 5x^2 - 32x + 51 = 0. Roots: x = [32 +/- sqrt(1024 - 1020)] / 10 = (32 +/- 2) / 10. x = 3.4 or 3. Eq II: y^2 = 9, so y = 3 or -3. Comparing: x=3.4, y=3 (x>y); x=3.4, y=-3 (x>y); x=3, y=3 (x=y); x=3, y=-3 (x>y). Thus x >= y.

AI explanation

For the first equation, five x squared minus thirty two x plus fifty one equals zero, factoring gives five x minus fifteen times x minus three point four equals zero, meaning the roots are three and three point four. For the second equation, y squared minus nine equals zero, taking the square root gives y equals positive three or negative three. Comparing the roots, both values of x, which are three and three point four, are greater than or equal to the maximum value of y, which is three. Therefore, the relation x is greater than or equal to y holds true.

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